mcl(1)                           USER COMMANDS                          mcl(1)



  NAME
      mcl - The Markov Cluster Algorithm, aka the MCL algorithm.

  SYNOPSIS
      mcl  <-|fname>  [-I f (inflation)] [-o str (fname)] [-scheme k (resource
      scheme)]

      These options are sufficient in 95 percent of the  cases  or  more.  The
      first  argument  must be the name of a file containing a graph/matrix in
      the mcl input format, or a hyphen to read from STDIN.  With  respect  to
      clustering,  only  the -I option and -scheme option are relevant and the
      rest is immaterial.

      As of the first 1.002 release, mcl will accept a very general input for-
      mat.  Graph indices no longer need be sequential; you can use any set of
      indices you like, as long as they are in a suitable range. Refer to  the
      mcxio(5)  section,  and  use mcl -z to find the range from which indices
      can be picked.

      As of the first 1.003 release, clmformat enables you to map a clustering
      onto  a format better suited for inspection, using an index file (the so
      called tab file) mapping mcl indices onto descriptive labels.  Read  the
      clmformat manual for more information - it is simple to use and the man-
      ual is small.

      A mechanism for pipelines is supported (as of the first 1.003  release).
      Refer  to  the  PIPELINES  section  for more information.  A prepackaged
      pipeline for BLAST data is present in the form of mclblastline.

      The full listing of mcl options is shown  below,  separated  into  parts
      corresponding  with  functional  aspects  such as clustering, threading,
      verbosity, pruning and resource management, automatic output naming, and
      dumping.   The  -scheme  parameter provides a single access point to the
      pruning options, and should be sufficient in  most  cases.   mcl  allows
      comprehensive  tuning  and  access  to  its  internals for those who are
      interested, so it has many options.

      Baseline clustering options
      [-I f (inflation)] [-o str (fname)] [-scheme k (resource scheme)]

      Additional clustering options
      [-l n (initial iteration number)] [-L n (main iteration number)]  [-i  f
      (initial inflation)]

      Input manipulation options
      [-c  f  (centering)]  [-pi  f  (pre-inflation)] [-pp n (preprune count)]
      [-in-gq f (filter threshold)]

      Alternative modes
      [--expand-only (factor out computation)] [--inflate-first  (rather  then
      expand)]

      Clustering result options
      [-sort str (sort mode)] [--keep-overlap=y/n (retain overlap)] [--output-
      limit=y/n (write limit matrix)] [--force-connected=y/n  (analyze  compo-
      nents)]   [--check-connected=y/n  (analyze  components)]  [--analyze=y/n
      (performance criteria)] [--show-log=y/n  (show  log)]  [--append-log=y/n
      (append log)]

      Verbosity options
      [-v  str  (verbosity  type  on)] [-V str (verbosity type off)] [--silent
      (very)] [--verbose (very)] [-progress k (gauge)] [--show (print  (small)
      matrices to screen)]

      Thread options
      [-te  k  (#expansion  threads)]  [-ti  k  (#inflation  threads)]  [-t  k
      (#threads)] [--clone (when threading (experimental))] [-cloneat n (trig-
      ger)]

      Output file name options
      [-o  str  (fname)]  [-ap  str  (use  str  as file name prefix)] [-aa str
      (append str to suffix)] [-az (show output  file  name  and  exit)]  [-ax
      (show output suffix and exit)]

      Dump options
      [-dump-interval  i:j  (dump  interval)]  [-dump-modulo  k (dump modulo)]
      [-dump-stem stem (dump file stem)] [-dump str (type)]  [-dump-subi  spec
      (index  list for submatrix dump)] [-dump-subd spec (domain list for sub-
      matrix dump)] [-dump-dom fname (domain matrix file)] [-digits n  (print-
      ing precision)]

      Info options
      [--jury-charter  (explains jury)] [--version (show version)] [-how-much-
      ram k (RAM upper bound)] [-h (most important options)] [--apropos  (one-
      line  description  for  all  options)] [-z (show current settings)] [-az
      (show output file name and exit)] [-ax (show output  suffix  and  exit)]
      [--show-schemes (show resource schemes)]

      Pruning options
      The following options all pertain to the various pruning strategies that
      can be employed by mcl. They are described in the PRUNING  OPTIONS  sec-
      tion, accompanied by a description of the mcl pruning strategy.  If your
      graphs are huge and you have an appetite for tuning, have a look at  the
      following:

      [-p  f  (cutoff)]  [-P  n  (1/cutoff)]  [-S  n (selection number)] [-R n
      (recovery number)] [-pct f (recover percentage)] [-my-scheme n (tag cus-
      tom  scheme)]  [-warn-pct  n  (prune  warn  percentage)] [-warn-factor n
      (prune warn factor)] [--dense (allow matrices to fill)] [--adapt  (prun-
      ing)]  [--rigid  (pruning)]  [-ae  f (adaptive pruning exponent)] [-af f
      (adaptive pruning factor)] [-nx x (x window index)]  [-ny  y  (y  window
      index)]  [-nj  j (jury window index)] [-nw w (nr of windows)] [-nl w (nr
      of iterations)] [--thick (expect dense input graph)]

      The first argument of mcl must be a file  name,  but  some  options  are
      allowed  to  appear as the first argument instead. These are the options
      that cause mcl to print out information of some  kind,  after  which  it
      will gracefully exit. The full list of these options is

      -z,  -h,  --apropos, --version, --show-settings, --show-schemes, --jury-
      charter, -how-much-ram k.

  DESCRIPTION
      mcl implements the MCL algorithm, short for  the  Markov  cluster  algo-
      rithm,  a  cluster algorithm for graphs developed by Stijn van Dongen at
      the Centre for  Mathematics  and  Computer  Science  in  Amsterdam,  the
      Netherlands.  The  algorithm  simulates  flow using two simple algebraic
      operations on matrices.  The inception of this flow process and the the-
      ory behind it are described elsewhere (see REFERENCES). Frequently asked
      questions are answered in the mclfaq(7) section.  The program  described
      here  is  a fast threaded implementation written by the algorithm's cre-
      ator with contributions by several others. Anton Enright  co-implemented
      threading;  see the HISTORY/CREDITS section for a complete account.  See
      the APPLICABILITY section for a description of the  type  of  graph  mcl
      likes  best,  and  for  a  qualitative  assessment of its speed.  mcl is
      accompanied by several other utilities  for  analyzing  clusterings  and
      performing matrix and graph operations; see the SEE ALSO section.

      The  first argument is the input file name (see the mcxio(5) section for
      its expected format), or a single hyphen to read from stdin. The  ratio-
      nale for making the name of the input file a fixed parameter is that you
      typically do several runs with different  parameters.  In  command  line
      mode it is pleasant if you do not have to skip over an immutable parame-
      ter all the time.

      The -I f option is the  main  control,  affecting  cluster  granularity.
      Using  mcl  is  as simple as typing (assuming a file proteins contains a
      matrix/graph in mcl input format)

      mcl proteins -I 2.0

      The above will result in a clustering written to the file named out.pro-
      teins.I20s2. It is - of course - possible to explicitly specify the name
      of the output file using the -o option. Refer to the  -ap option  for  a
      description  of mcl's procedure in automatically constructing file names
      from it parameters.

      The mcl input format is described in the mcxio(5)  section.  Clusterings
      are  also  stored  as matrices - this is again discussed in the mcxio(5)
      section.  You presumably want to convert the output to something that is
      easier  to  interpret.  The  mcl  matrix format is perhaps unpleasant to
      parse in the quick and dirty way. You can use

      clmformat -icl <mcl-out-file> -dump -

      to convert mcl output to a line/tab based format, where each lines  con-
      tains  a  cluster  in the form of tab-separated indices. If you throw in
      the -tab <tab-file> option, you can get tab-separated labels.  Refer  to
      the clmformat manual page for more information.

      In  finding  good  mcl parameter settings for a particular domain, or in
      finding cluster structure at different levels of granularity, one  typi-
      cally  runs  mcl  multiple  times  for varying values of f (refer to the
      -I option for further information).

      mcl expects a nonnegative matrix in the input file, or  equivalently,  a
      weighted  (possibly  directed)  graph.  NOTE - mcl interprets the matrix
      entries or graph edge weights as similarities, and it  likes  undirected
      input  graphs  best.  It  can  handle directed graphs, but any node pair
      (i,j) for which w(i,j) is much smaller than w(j,i) or  vice  versa  will
      presumably  have a slightly negative effect on the clusterings output by
      mcl. Many such node pairs will have a distinctly negative effect, so try
      to make your input graphs undirected. How your edge weights are computed
      may affect mcl's performance. In protein clustering, one way to go is to
      choose  the  negated  logarithm  of  the BLAST probabilities (see REFER-
      ENCES).

      mcl's default parameters should make it quite fast under almost all cir-
      cumstances.  Taking  default  parameters,  mcl has been used to generate
      good protein clusters on 133k proteins, taking 10 minutes  running  time
      on  a  Compaq  ES40 system with four alpha EV6.7 processors. It has been
      applied (with good results) to graphs with 800k nodes, and if  you  have
      the  memory  (and  preferably CPUs as well) nothing should stop you from
      going further.

      For large graphs, there are several groups of parameters  available  for
      tuning  the  mcl  computing process, should it be necessary. The easiest
      thing to do is just vary the -scheme  option.  This  triggers  different
      settings  for the group of pruning parameters {-p/-P, -R, -S, and -pct}.
      The default setting corresponds with -scheme 4.  There is an  additional
      group  of  control parameters {--adapt, --rigid, -ae, -af}, which may be
      helpful in speeding up mcl.  When doing multiple mcl runs for  the  same
      graphs  with different -I settings (for obtaining clusterings at differ-
      ent levels of granularity), it can be useful to factor out the first bit
      of  computation  that  is common to all runs, by using the --expand-only
      option one time and then using --inflate-first for each run in the  set.
      Whether  mcl considers a graph large depends mainly on the graph connec-
      tivity; a highly connected graph on 50,000 nodes is  large  to  mcl  (so
      that  you  might  want  to  tune resources) whereas a sparsely connected
      graph on 500,000 nodes may be business as usual.

      mcl is a memory munger. Its precise appetite  depends  on  the  resource
      settings.  You  can get a rough (and usually much too pessimistic) upper
      bound for the amount of RAM that is needed by  using  the  -how-much-ram
      option.  The corresponding entry in this manual page contains the simple
      formula via which the upper bound is computed.

      Two other groups of interest are the  thread-related  options  (you  can
      specify  the number of threads to use) {-t, -te, -ti, --clone, -cloneat}
      and the verbosity-related options {--verbose, --silent,  -v,  -V}.   The
      actual  settings are shown with -z, and for graphs with at most 12 nodes
      or so you can view the MCL matrix iterands on screen by supplying --show
      (this may give some more feeling).

      MCL  iterands allow a generic interpretation as clusterings as well. The
      clusterings associated with early iterands may contain a fair amount  of
      overlap.  Refer to the -dump option, the mclfaq(7) manual, and the clmi-
      mac utility (Interpret Matrices As Clusterings).  Use  clmimac  only  if
      you  have  a  special  reason; the normal usage of mcl is to do multiple
      runs for varying -I parameters and use the  clusterings  output  by  mcl
      itself.

      Under  very rare circumstances, mcl might get stuck in a seemingly infi-
      nite loop. If the number of iterations exceeds a hundred and  the  chaos
      indicator  remains  nearly  constant (presumably around value 0.37), you
      can force mcl to stop by sending it the ALRM  signal  (usually  done  by
      kill  -s  ALRM pid). It will finish the current iteration, and interpret
      the last iterand a clustering. Alternatively, you can wait and mcl might
      converge  by  itself  or  it will certainly stop after 10,000 iterations
      (the default value for the -L option). The most probable explanation for
      such  an  infinite  loop  is that the input graph contains the flip-flop
      graph of node size three as a subgraph.

      The creator of  this  page  feels  that  manual  pages  are  a  valuable
      resource,  that  online html documentation is also a good thing to have,
      and that info pages are way way ahead of their time. The  NOTES  section
      explains how this page was created.

      In  the  OPTIONS section options are listed in order of importance, with
      related options grouped together.

  OPTIONS
      -I f (inflation)
         Sets the main inflation value to f. This value is the main handle for
         affecting  cluster granularity. It is usually chosen somewhere in the
         range [1.2-5.0]. -I 5.0 will tend to result in fine-grained  cluster-
         ings,  and -I 1.2 will tend to result in very coarse grained cluster-
         ings. Your mileage will vary depending on the characteristics of your
         data. That is why it is a good idea to test the quality and coherency
         of your clusterings using clmdist and clminfo. This will most  likely
         reveal  that certain values of -I are simply not right for your data.
         The clmdist section contains a discussion of how to use  the  cluster
         validation tools shipped with mcl (see the SEE ALSO section).

         A  second  option for affecting cluster granularity is the -c option.
         It may possibly increase granularity.

         With low values for -I, like -I 1.2, you should be  prepared  to  use
         more  resources  in  order  to  maintain quality of clusterings, i.e.
         increase the argument to the -scheme option.

      -o str (fname)
         Output the clustering to file named fname.  It is  possible  to  send
         the  clustering to stdout by supplying -o -. The clustering is output
         in the mcl matrix format; see the mcxio(5) section for more  informa-
         tion on this.

         Look at the -ap option and its siblings for the automatic naming con-
         structions employed by mcl if the -o option is not used.

      -scheme k (use a preset resource scheme)
         There are currently seven different resource schemes,  indexed  1..7.
         High  schemes result in more expensive computations that may possibly
         be more accurate. The default scheme is 4. When mcl is done, it  will
         give  a grade (the so called jury synopsis) to the appropriateness of
         the scheme used. A low grade does  not  necessarily  imply  that  the
         resulting  clustering is bad - but anyway, a low grade should be rea-
         son to try for a higher scheme. The grades are listed in the  PRUNING
         OPTIONS section under the -nj option.

         The  PRUNING OPTIONS section contains an elaborate description of the
         way mcl manages resources, should you be interested.  In case you are
         worried  about  the  validation  of  the  resulting  clusterings, the
         mclfaq(7) section has several entries discussing this issue. The bot-
         tom  line  is that you have to compare the clusterings resulting from
         different schemes (and otherwise identical parameters)  using  utili-
         ties  such  as  clmdist,  clminfo on the one hand, and your own sound
         judgment on the other hand.

         If your input graph is extremely dense, with an average  node  degree
         (i.e. the number of neighbours per node) that is somewhere above 500,
         you may need to filter the input graph by removing the nodes of high-
         est  degree  (and  projecting them back onto the resulting clustering
         afterwards) or by using the -pp option.

      --show-schemes (show preset resource schemes)
         Shows the explicit settings to which  the  different  preset  schemes
         correspond.

         The  characteristics are written in the same format (more or less) as
         the output triggered by -v pruning.

      -c f (centering)
         The larger the value of f the more nodes are attached  to  themselves
         rather  than  their  neighbours, the more expansion (the spreading of
         flow through the graph) is opposed, and the more  fine-grained  clus-
         terings  tend to be. f should be chosen greater than or equal to 1.0.
         The default is f=1.0. This option has a much weaker effect  than  the
         -I option, but it can be useful depending on your data.

      -v str (verbosity type on)
         See the --verbose option below.

      -V str (verbosity type off)
         See the --verbose option below.

      --silent (very)
         See the --verbose option below.

      --verbose (very)
         These are the different verbosity modes:

         progress
         pruning
         explain
         all

         where  all means all three previous modes.  --verbose and -v all turn
         them all on, --silent and -V all turn them all off. -v str and -V str
         turn  on/off  the  single mode str (for str equal to one of progress,
         pruning, or explain).  Each verbosity mode is  given  its  own  entry
         below.

      -v progress
         This  mode  causes  mcl to emit an ascii gauge for each single matrix
         multiplication. It uses some default length for the gauge, which  can
         be  altered  by  the -progress k option. Simply using the latter will
         also turn on this verbosity mode.  This mode can give you quickly  an
         idea how long an mcl run might take. If you use threading (see the -t
         option and its friends), this option may slow down the program a lit-
         tle  (relative to -V progress, not relative to a single-CPU mcl run).

      -v explain
         This mode causes the output of explanatory headers  illuminating  the
         output generated with the pruning verbosity mode.

      -v pruning
         This mode causes output of resource-related quantities. It has a sep-
         arate entry in the PRUNING OPTIONS section.

      -progress k (gauge)
         If k>0 then for each matrix multiplication mcl will  print  an  ascii
         gauge telling how far it is. The gauge will be (in some cases approx-
         imately) k characters long. If k<0 then mcl will emit a gauge that is
         extended by one character after every |k| vectors computed. For large
         graphs, this option has been known to ease the pain of impatience. If
         k=0 then mcl will print a message only after every matrix multiplica-
         tion, and not during matrix multiplication. This can be  useful  when
         you want mcl to be as speedy as possible, for example when using par-
         allellized mode (as monitoring progress  requires  thread  communica-
         tion).  For parallellization (by threading) see the -t option.

      -aa str (append str to suffix)
         See the -ap option below.

      -ap str (use str as file name prefix)
         If  the -o option is not used, mcl will create a file name (for writ-
         ing output to) that should uniquely characterize the important param-
         eters  used  in  the current invocation of mcl. The default format is
         out.fname.suf, where out is simply the literal string out,  fname  is
         the  first  argument containing the name of the file (with the graph)
         to be clustered, and where suf is the suffix encoding a set of param-
         eters (described further below).

         The -ap str option specifies a prefix to use rather than out.fname as
         sketched above.  However, mcl will interpret the  character  '=',  if
         present in str, as a placeholder for the input file name.

         If  the -aa str option is used, mcl will append str to the suffix suf
         created by itself.  You can use this if you need to encode some extra
         information in the file name suffix.

         The  suffix is constructed as follows. The -I f and -scheme parameter
         are always encoded.  The -pi f, -l k, -i f, and -c f options are only
         encoded  if  they  are  used.  Any  real  argument f is encoded using
         exactly one trailing digit behind the decimal separator (which itself
         is  not  written).  The  setting  -I 3.14 is thus encoded as I31. The
         -scheme option is encoded using the letter  's',  all  other  options
         mentioned  here  are  encoded as themselves (stripped of the hyphen).
         For example

         mcl small.mci -I 3 -c 2.5 -pi 0.8 -scheme 5

         results in the file name out.small.mci.I30s5c25pi08.  If you want  to
         know  beforehand what file name will be produced, use the -az option.

      -az (show output file name and exit)
      -ax (show output suffix and exit)
         If mcl automatically constructs a file name, it  can  be  helpful  to
         known  beforehand  what  that file name will be. Use -az and mcl will
         write the file name to STDOUT and exit. This can be used  if  mcl  is
         integrated  into  other  software for which the automatic creation of
         unique file names is convenient.

         By default MCL incorporates the input file name into the output  file
         name  and appends a short suffix describing the most important option
         settings. Use -ax to find out what that suffix is.  This can be  use-
         ful in wrapper pipeline scripts such as clxcoarse.

      -te k (#expansion threads)
         See the -t k option below.

      -ti k (#inflation threads)
         See the -t k option below.

      --clone (when threading)
         See the -t k option below.

      -cloneat n (trigger)
         See the -t k option below.

      -t k (#threads)
         The -t options are self-explanatory. Note that threading inflation is
         hardly useful, as inflation is orders of magnitude faster than expan-
         sion.  Also  note  that threading is only useful if you have a multi-
         processor system.

         The --clone option says to give each  thread  its  own  copy  of  the
         matrix  being expanded/squared. The latter option can be further con-
         trolled using the --cloneat k option. Copies are  only  made  if  the
         source matrix (the one to be squared) has on average at least k posi-
         tive entries per vector. This option is  probably  not  very  useful,
         because without it mcl is a memory munger already.

         When  threading,  it is best not to turn on pruning verbosity mode if
         you are letting mcl run unattended, unless you want to scrutinize its
         output  later.  This  is  because  it  makes mcl run somewhat slower,
         although the difference is not dramatic.

      -l n (initial iteration number) (small letter ell)
         The number of times mcl will use a different inflation  value  before
         it  switches  to  the  (main) inflation given by the -I (capital eye)
         option. The different value is called initial inflation and  is  tun-
         able  using  the -i f option (default value f=2.0). The default value
         (to -l) is zero. This option supplies new ways of  affecting  cluster
         granularity, e.g. by supplying

         mcl proteins -i 1.4 -l 2 -I 4.0

         one  lets expansion prevail during the first two iterations, followed
         by inflation catching up (in a figurative way of writing).  This  may
         be  useful in certain cases, but this type of experiment is certainly
         secondary to simply varying -I (capital eye).

      -L n (main iteration number)
         Normally, mcl computes the MCL process until it has  converged  fully
         to  a  doubly idempotent matrix. The number of iterations required is
         typically somewhere in the range 10-100.  The  first  few  iterations
         generally  take the longest time.  The -L option can be used to spec-
         ify the number of iterations mcl may do at most. When this number  is
         reached,  mcl  will output the clustering associated with the iterand
         last computed.

      -i f (initial inflation)
         The inflation value used during the first n iterations,  where  n  is
         specified by the -l (ell) option.  By default, n=0 and f=2.0.

      -pi f (pre-inflation)
         If  used, mcl will apply inflation one time to the input graph before
         entering the main process. This can be useful  for  making  the  edge
         weights  in a graph either more homogeneous (which may result in less
         granular clusterings) or more heterogeneous (which may result in more
         granular  clusterings).   Homogeneity  is  achieved for values f less
         than one, heterogeneity for values larger than one.   Values  to  try
         are normally in the range [2.0,10.0].

      -di i:j (dump interval)
      -dump-interval i:j
         Dump during iterations i..j-1. See the -dump str option below.

      -dm k (dump i+0..i+k..)
      -dump-modulo k
         Sampling  rate:  select  only  these iterations in the dump interval.
         See the -dump str option below.

      -ds stem (file stem)
      -dump-stem stem
         Set the the stem for file names of dumped objects (default mcl).  See
         the -dump str option below.

      -dump-subi spec (index list for submatrix dump)
      -dump-subd spec (domain list for submatrix dump)
      -dump-dom fname (domain matrix file)
         -dump-subi  specifies a range of indices which will be used to select
         the extended principal submatrix.  Argument spec can be a comma-sepa-
         rated  list of single integers and integer ranges. Ranges are denoted
         by two integers separated by a hyphen.

         If -dump-dom is used and specifies a matrix file, the indices  speci-
         fied  in  the  -dump-subd option should index columns in that matrix.
         These columns are merged and added to the list  of  entries  used  in
         selecting the extended principal submatrix.

      -dump str (type)
         str can be of the following types.

         ite
         dag
         cls
         chr

         Repeated use is allowed.  The ite option writes mcl iterands to file.
         The cls option writes clusterings associated  with  mcl  iterands  to
         file.  These clusters are obtained from a particular directed acyclic
         graph (abbreviated as DAG) associated  with  each  iterand.  The  dag
         option  writes  that  DAG  to file. The DAG can optionally be further
         pruned and then again be interpreted as a clustering  using  clmimac,
         and  clmimac  can  also  work with the matrices written using the ite
         option.  It should be noted that clusterings associated with interme-
         diate  iterands  may  contain  overlap,  which is interesting in many
         applications. For more information refer to mclfaq(7) and the  REFER-
         ENCES section below.

         The  chr  option  says, for each iterand I, to output a matrix C with
         characteristics of I. C has the same number of columns as I. For each
         column  k in C, row entry 0 is the diagonal or 'loop' value of column
         k in  I  after  expansion  and  pruning,  and  before  inflation  and
         rescaling.  Entry  1 is the loop value after inflation and rescaling.
         Entry 2 is the center of column k (the sum of  its  entries  squared)
         computed  after  expansion and before pruning, entry 3 is the maximum
         value found in that column at the same time. Entry 4 is the amount of
         mass kept for that column after pruning.

         The  -ds  option  sets  the  stem  for  file  names of dumped objects
         (default mcl). The -di and -dm options allow a selection of  iterands
         to be made.

      -digits n (printing precision)
         This  has  two completely different uses. It sets the number of deci-
         mals used for pretty-printing mcl  iterands  when  using  the  --show
         option (see below), and it sets the number of decimals used for writ-
         ing the expanded matrix when using the --expand-only option.

      --show (print matrices to screen)
         Print matrices to screen. The number  of  significant  digits  to  be
         printed  can  be  tuned  with  -digits n.  An 80-column screen allows
         graphs (matrices) of size up to 12(x12) to be printed with three dig-
         its  precision (behind the comma), and of size up to 14(x14) with two
         digits. This can give you an idea of how mcl operates, and  what  the
         effect  of pruning is.  Use e.g. -S 6 for such a small graph and view
         the MCL matrix iterands with --show.

      -sort str (sort mode)
         str can be one of lex, size, revsize, or none. The default  is  'rev-
         size',  in  which  the  largest  clusters  come first. If the mode is
         'size', smallest clusters come first, if the mode is 'lex',  clusters
         are  ordered  lexicographically, and if the mode is 'none', the order
         is the same as produced by the procedure used by mcl to map  matrices
         onto clusterings.

      --keep-overlap y/n (retain overlap)
         The  keep-overlap  action  causes  mcl  to retain overlap should this
         improbable event occur. In theory, mcl may generate a clustering that
         contains  overlap, although this almost never happens in practice, as
         it requires some particular type of symmetry to  be  present  in  the
         input  graph  (not just any symmetry will do).  Mathematically speak-
         ing, this is a conjecture and not a theorem, but the  present  author
         wil  eat  his  shoe  if  it  fails to be true (for marzipan values of
         shoe). It is easy though to construct an input graph for  which  cer-
         tain  mcl settings result in overlap - for example a line graph on an
         odd number of nodes. The default  is  to  remove  overlap  should  it
         occur.

         This option has more than theoretical use because mcl is able to gen-
         erate clusterings associated with intermediate iterands.   For  these
         clusterings, overlap is more than a theoretical possibility, and will
         often occur. If you specify the -L k  option,  mcl  will  output  the
         clustering associated with the last iterand computed, and it may well
         contain overlap.

         This option has no effect on the clusterings  that  are  output  when
         using  -dump cls  -  the  default  for  those  is that overlap is not
         touched, and this default can not yet be overridden.

      --force-connected=y/n (analyze components)
      --check-connected=y/n (analyze components)
         If the input graph has  strong  bipartite  characteristics,  mcl  may
         yield  clusters that do not correspond to connected components in the
         input graph. Turn one of these modes  on  to  analyze  the  resultant
         clustering.

         If  loose clusters are found they will be split into subclusters cor-
         responding to connected  components.   With  --force-connected=y  mcl
         will  write  the  corrected clustering to the normal output file, and
         the old clustering to the same file with suffix orig.  With  --check-
         connected=y  mcl will write the loose clustering to the normal output
         file, and the corrected clustering to the same file with suffix coco.

         These  options  are  not  on by default, as the analysis is currently
         (overly) time-consuming and mcl's behaviour actually makes some sense
         (when taking bipartite characteristics into account).

      --output-limit=y/n (write limit matrix)
         This will write the limit matrix to a file named base-limit.

      --analyze=y/n (performance criteria)
         With  this  mode turned on, mcl will reread the input matrix and com-
         pute a few performance criteria and attach them to the  output  file.
         Off by default.

      --append-log=y/n (append log)
         Appends  a  log  with the process characteristics to the output file.
         By default, this mode is on.

      --show-log=y/n (show log)
         Shows the log with process characteristics on  STDOUT.   By  default,
         this mode is off.

      --inflate-first (rather then expand)
         Normally,  mcl  will take the input graph/matrix, make it stochastic,
         and start computing an mcl process, where expansion and inflation are
         alternated.  This option changes that to alternation of inflation and
         expansion, i.e. inflation is the first operator to be  applied.  This
         is  intended for use with an input matrix that was generated with the
         --expand-only option (see below).  If you do multiple  mcl  runs  for
         the  same  graph,  then the first step will be the same for all runs,
         namely computing the square of the input matrix.  With  the  pair  of
         --inflate-first  and  --expand-only this bit of computing can be fac-
         tored out.  NOTE  this  option  assumes  that  the  input  matrix  is
         stochastic  (as  it  will be when generated with --expand-only).  The
         --inflate-first option renders all options useless that  will  other-
         wise  affect  the input matrix, and precisely these options do affect
         the matrix resulting from using --expand-only. See  the  entry  below
         for more information.

      --expand-only (factor out computation)
         This   option  makes  mcl  compute  just  the  square  of  the  input
         graph/matrix, and write it to the file  name  supplied  with  the  -o
         flag,  or  to  the  default file named out.mce. NOTE in this case the
         output matrix is not a clustering. The intended use is that the  out-
         put  matrix  is used as input for mcl with the --inflate-first switch
         turned on, so that multiple mcl runs need not redo the same  computa-
         tion (the first expansion step).

         Note  that  the  -scheme  parameters  affect the matrix computed with
         --expand-only. Other options that affect the  matrix  resulting  from
         this  option: -pp, -c, and -digits. The latter option sets the preci-
         sion for output in native ascii format.

      -in-gq f (filter threshold)
         mcl will remove any edges in the input graph  (equivalently,  entries
         in the input matrix) for which the weight is below f.

      -pp n (preprune count)
         For  each  column  vector (node) in the input matrix (graph) mcl will
         keep the n entries (outgoing edges) of that vector (node)  that  have
         largest weight and remove the rest.

      --jury-charter (explains jury)
         Explains how the jury synopsis is computed from the jury marks.

      --version (show version)
         Show version.

      -how-much-ram n (RAM upper bound)
         n  is interpreted as the number of nodes of an input graph.  mcl will
         print the maximum amount of RAM it needs for its  computations.   The
         formula for this number in bytes is:

            2 * c * k * n

            2  :  two matrices are concurrently held in memory.
            c  :  mcl cell size (as shown by -z).
            n  :  graph cardinality (number of nodes).
            k  :  MAX(s, r).
            s  :  select number (-S, -scheme options).
            r  :  recover number (-R, -scheme options).

         This  estimate will usually be too pessimistic. It does assume though
         that the average node degree of the input graph does  not  exceed  k.
         The  -how-much-ram  option  takes  other  command-line arguments into
         account (such as -S and -R), and it expresses the amount  of  RAM  in
         megabyte units.

      -h (show help)
         Shows a selection of the most important mcl options.

      --apropos (show help)
         Gives a one-line description for all options.

      --show-settings (show settings)
         A synonym for the -z option.

      -z (show settings)
         Show  current  settings for tunable parameters.  --show-settings is a
         synonym.

  PRUNING OPTIONS
      -p f (cutoff)
      -P n (1/cutoff)
      -S s (selection number)
      -R r (recover number)
      -pct pct (recover percentage)
      -my-scheme n (tag custom scheme)
         After computing a new (column stochastic) matrix vector during expan-
         sion  (which  is  matrix multiplication c.q. squaring), the vector is
         successively exposed to different pruning strategies. The  intent  of
         pruning  is  that many small entries are removed while retaining much
         of the stochastic mass of the original vector. After pruning, vectors
         are  rescaled  to be stochastic again. MCL iterands are theoretically
         known to be sparse in a weighted sense, and this manoever effectively
         perturbs  the  MCL  process a little in order to obtain matrices that
         are genuinely sparse, thus  keeping  the  computation  tractable.  An
         example  of  monitoring  pruning  can  be  found in the discussion of
         -v pruning at the end of this section.

         mcl proceeds as follows. First, entries that are smaller than  cutoff
         are removed, resulting in a vector with at most 1/cutoff entries. The
         cutoff can be supplied either by -p, or as the inverse value  by  -P.
         The latter is more intuitive, if your intuition is like mine (and the
         P stands for precision or pruning  by  the  way).   The  cutoff  just
         described  is  rigid;  it  is  the  same for all vectors. The --adapt
         option causes the computation of a cutoff that depends on a  vector's
         homogeneity  properties, and this option may or may not speed up mcl.

         Second, if the remaining stochastic mass (i.e. the sum of all remain-
         ing entries) is less than pct/100 and the number of remaining entries
         is less than r (as specified by the -R flag), mcl will try to  regain
         ground  by recovering the largest discarded entries. The total number
         of entries is not allowed to grow larger than r.  If recovery was not
         necessary,  mcl  tries  to prune the vector further down to at most s
         entries (if applicable), as specified by the -S flag. If this results
         in  a  vector  that satisfies the recovery condition then recovery is
         attempted, exactly as described above. The latter will not  occur  of
         course if r <= s.

         The  default  setting  is something like -P 4000 -S 500 -R 600. Check
         the -z flag to be sure. There is a set of precomposed settings, which
         can  be  triggered  with  the  -scheme k  option.  k=4 is the default
         scheme; higher values for k result in costlier and more accurate com-
         putations  (vice  versa  for lower, cheaper, and less accurate).  The
         schemes are listed using the --show-schemes option. It  is  advisable
         to  use  the  -scheme option only in interactive mode, and to use the
         explicit expressions when doing batch processing. The reason is  that
         there  is  no  guarantee  whatsoever that the schemes will not change
         between different releases. This is because the scheme options should
         reflect  good  general purpose settings, and it may become appararent
         that other schemes are better.

         Note that 'less accurate' or 'more accurate' computations  may  still
         generate  the  same output clusterings. Use clmdist to compare output
         clusterings for different resource parameters. Refer to clmdist for a
         discussion of this issue.

         The  -my-scheme n  option sets a tag that is used in constructing the
         default output naming file. If not used, mcl will create a relatively
         long  string  describing  the  settings  of  the -P, -pct, -R, and -S
         parameters, e.g. P600Q85R1000S1200 (where Q tags  the  pct  setting).
         If used, mcl will simply use the tag sn.

      -warn-pct k (prune warn percentage)
      -warn-factor k (prune warn factor)
         The  two  options  -warn-pct and -warn-factor relate to warnings that
         may be triggered once the initial pruning of a vector  is  completed.
         The  idea  is  to issue warnings if initial pruning almost completely
         destroys a computed vector, as this may be a sign  that  the  pruning
         parameters  should be changed. It depends on the mass remaining after
         initial pruning whether a warning will be issued.  If  that  mass  is
         less  than  warn-pct or if the number of remaining entries is smaller
         by a factor warn-factor than both the number  of  entries  originally
         computed  and  the  recovery  number,  in that case, mcl will issue a
         warning.

         -warn-pct takes an integer between 0 and 100 as parameter, -warn-fac-
         tor  takes  a real positive number. They default to something like 30
         and 50.0. If you want to see less  warnings,  decrease  warn-pct  and
         increase  warn-factor.  Set  warn-factor to zero if you want no warn-
         ings.

      --dense (allow matrices to fill)
         This renders all pruning options useless except for one.  After  each
         expansion step, mcl will remove all entries that are smaller than the
         threshold specified by -p or -P, which acts like a precision in  this
         case. After removal, the matrix columns are rescaled to be stochastic
         again.

         If the -p threshold (precision) is zero or very  small,  the  --dense
         option  results  in  a rather accurate and very costly computation of
         the MCL process. Do not use this option for  graphs  with  more  than
         several  thousands  of entries, or you will have trouble digging your
         processor out of swap.

      --rigid (pruning)
         See the --adapt option below.

      -ae f (adaptive pruning exponent)
         See the --adapt option below.

      -af f (adaptive pruning factor)
         See the --adapt option below.

      --adapt (pruning)
         The default mcl pruning behaviour as described under the -P option is
         called rigid pruning (it being the default renders the switch --rigid
         currently useless), refering to the fact  that  the  first  stage  of
         pruning  removes entries smaller than a fixed threshold.  The options
         discussed here enable the computation of a threshold that depends  on
         the  homogeneity characteristics of a vector. This behaviour is trig-
         gered by supplying --adapt.

         The --adapt behaviour only affects the first pruning stage, c.q.  the
         computation  of  the first threshold (see the discussion under the -P
         option). It does not interfere with either selection or recovery.  It
         is  affected  however by the threshold as specified by the -P option.
         When using --adapt, you typically use the -P option as well, and  you
         can  and  should  use  a  higher  value  then you would without using
         --adapt.

         All that said, --adapt triggers this behaviour:  Given  a  stochastic
         vector  v, its mass center of order two is computed, which is the sum
         of each entry squared. The mass center of v, call it c,  is  strongly
         related to its homogeneity properties (see REFERENCES). The threshold
         T is computed as 1/f * pow(c, e), where e and f are the arguments  to
         the -af f and -ae e options respectively (check -z for the respective
         defaults).  For either e or f decreasing  it  means  that  T  becomes
         larger.   Finally,  T  is maxed with the rigid threshold value, which
         can be altered using either -p f or -P n.   The  latter  is  why  you
         should  increase  the  -P parameter n (so that the rigid threshold is
         decreased) once you switch to adaptive pruning. The adaptive  thresh-
         old  should  be  the  main factor controlling pruning, with the rigid
         threshold acting as a safeguard that does not take over too often.

         This may seem complicated, but the rules are actually  quite  simple,
         and  you  may  just  disregard the definition of T. The usefulness of
         these options will vary. If you want to speed up mcl, try it out  and
         add --adapt to your settings.

      --thick (expect dense input graph)
         This  option is somewhat esoteric. It does not affect the matrices as
         computed by mcl, but it affects the way in which they  are  computed.
         If the input graph is very dense, this may speed up mcl a little.

      -v pruning
         Pruning  verbosity mode causes mcl to emit several statistics related
         to the pruning  process,  each  of  which  is  described  below.  Use
         -v explain  to get explanatory headers in the output as well (or sim-
         ply use -v all).

         Selection and recovery
         The number of selections and recoveries mcl  had  to  perform  during
         each  iteration  is  shown.  It  also shows the number of vectors for
         which the mass after final pruning was below the fraction defined  by
         the -pct option as a percentage (default probably 90 or 95).

         Initial and pruned vector footprint distributions
         The distribution of the vector footprints (i.e. the number of nonzero
         entries) before and after pruning is shown. This is  assembled  in  a
         terse (horrid if you will) format, looking as follows (with some con-
         text stripped, noting that the data  for  three  expansion  steps  is
         shown):

         ----------------------------------------------------
          mass percentages  | distr of vec footprints       |
                  |         |____ expand ___.____ prune ____|
           prune  | final   |e4   e3   e2   |e4  e3   e2    |
         all ny nx|all ny nx|8532c8532c8532c|8532c8532c8532c|
         ---------.---------.---------------.---------.-----.
          98 88 86  98 91 86 _________022456 ___________0234
          98 89 86  98 94 91 _______00245678 ___________0234
          98 90 89  99 95 94 _______00235568 ___________0234
          ...

         This  particular  output  was  generated  (and  truncated after three
         rounds of expansion and inflation) from clustering a protein graph on
         9058  nodes  with  settings  -I 1.4,  -P 2000,  -S 500,  -R 600,  and
         -pct 95.

         The header entries 8532c85.. indicate thresholds  going  from  80000,
         50000, 20000, 12500, 8000, all the way down to 300, 200, and 125. The
         character 'c' signifies the base 1.25 (for no apparent  reason).  The
         second entry '2' (after '0') on the first line signifies that roughly
         20 percent of  all  the  vectors  had  footprint  (#nonzero  entries)
         between 800 and 1250.  Likewise, 40 percent had footprint between 300
         and 500. The '0' entries signify a fraction somewhere  below  5  per-
         cent,  and the '@' entries signify a fraction somewhere above 95 per-
         cent.

         Two columns are listed, one for the expansion vector footprints (i.e.
         after  squaring), and the other for the vector footprints right after
         initial pruning took place (i.e. before selection and recovery, after
         either  adaptive  or  rigid  pruning).   This may give an idea of the
         soundness of the initial pruning process (overly  severe,  or  overly
         mild),  and  the  extent  to which you want to apply selection and/or
         recovery.

         Initial and final mass windows
         The mass averages of the pruned vectors  after  the  first  selection
         stage are shown, and the mass averages of the vectors as finally com-
         puted, i.e. after selection and recovery. Note that the latter corre-
         sponds  to  a different stage than what is shown for the vector foot-
         prints, if either selection or  recovery  is  turned  on.   For  both
         cases,  three  averages  are shown: the average over all vectors, the
         average over the worst x cases, and the  average  over  the  worst  y
         cases.  The mass averages are shown as percentages: '98' on the first
         line under the 'prune/all' column means that overall  98  percent  of
         the stochastic mass of the matrix was kept after pruning.

         This  example  demonstrates  that many entries could be removed while
         retaining much of the stochastic mass. The  effect  of  the  recovery
         (-R)  parameter is also clear: the final averages are higher than the
         initial averages, as a result of mcl undoing  some  overenthousiastic
         pruning.

         An  average  over  the  worst  k cases is called a window of width k;
         internally, mcl tracks many more such windows. The result of this can
         be  seen when using the --append-log=y option (which appends a log to
         the cluster output) or the --show-log=y option (which sends  the  log
         to  STDOUT).   From  a fixed set of windows those that are applicable
         are tracked, that is, all those windows for which the width does  not
         exceed  the  graph  cardinality.  The  windows  in the fixed set have
         respective sizes 1, 2, 5, 10, 20, 50, and  so  on  up  until  5000000
         (which makes 15 windows in all).

      -nx i (x window index)
      -ny j (y window index)
         The  options  -nx  and -ny both take an index in the range 1..15. The
         default values for -nx and -ny are respectively 4 and 7, denoting the
         fourth  and  seventh window of respective widths 10 and 100. They are
         used in the verbosity output as described above.

      -nj i (jury window index)
         The -nj denotes a window index in the same way as  -nx  and  -ny  do.
         This  particular  window  is used for computing the jury marks, which
         are the three number reported by mcl when it  is  done.  They  are  a
         reminder  of  the  existence  of  pruning and its importance for both
         speed and accuracy, and they are indicative rather than  authorative.

         These  jury marks are simply the respective mass averages in the jury
         window for the first three iterations. The  marks  are  even  further
         simplified  and  mapped to the jury synopsis, which is a single grade
         expressed as an adjective. The grades are,  in  decreasing  order  of
         achievement,  perfect  exceptional superior excellent good acceptable
         mediocre poor bad lousy miserable  awful  wretched  atrocious.  Doing
         'mcl  --jury-charter'  will  tell you how the jury marks map onto the
         jury synopsis.

         The jury marks should preferably be higher than 70. If  they  are  in
         the vicinity of 80 or 90, mcl is doing fine as far as pruning is con-
         cerned.  Choose a higher scheme if you think them too low.  For  very
         dense  graphs  that  do have strong cluster structure, the jury marks
         can sink as low as to the 30's and 40's, but the  clusterings  gener-
         ated  by  mcl may still be good. The marks and the synopsis grade the
         severity of pruning, not cluster quality. Note that the jury  becomes
         friendlier, resp. harsher when the -nj option is increased/decreased.

      -nw w (nr of windows)
         Normally, mcl will use all windows that have width smaller  than  the
         cardinality of the input graph. This option limits the set of windows
         to those w windows of smallest width.  This affects the  output  when
         setting --append-log=y output.

      -nl l (number of iterations)
         By  default,  mcl will log the window mass averages for the first ten
         iterations. This options sets  that  number  to l.   It  affects  the
         --append-log=y output.

  PIPELINES
      In  general,  clustering  requires  several stages; creating the matrix,
      running mcl, and displaying the result. The display stage  is  supported
      by  clmformat.  The  matrix creation stage often needs only be done once
      for a given data collection, followed by repeated runs of the other  two
      stages for varying inflation values and scheme settings.

      The  matrix  creation  stage  can  often be split up in two more stages,
      namely parsing a data file in some given format, and assembling a matrix
      from  the data bits and pieces, such as node indices and edge weights or
      even edge weight contributions.  The assembly step can be done by mcxas-
      semble,  which  allows  a  very  general  input  format and customizable
      behaviour in how the bits and pieces should be transformed to the  input
      graph.  This leaves the parse stage to be filled in.

      The  mclpipeline  script  implements a generic and customizable pipeline
      encapsulating the four stages  distinguished  here  (parsing,  assembly,
      clustering, display). It is possible to let only part of the pipeline be
      active, and many other features  are  supported.  The  IO  mechanism  is
      entirely  file based, and files are associated with parametrizations via
      file name extensions (by all means a simple mechanism).

      mclpipeline requires a single parse script to be specified.  It will  be
      plugged  into  the  pipeline  and  you  should be set to run.  The parse
      script  must  satisfy  the  interface  requirements  described  in   the
      mclpipeline manual page.

      For BLAST input, the mclblastline script provides a dedicated interface.
      It uses the mcxdeblast script that comes prepackaged with mcl.

  APPLICABILITY
      mcl will work very well for graphs in which the diameter of the  natural
      clusters  is not too large. The presence of many edges between different
      clusters is not problematic; as long as there is cluster structure,  mcl
      will  find  it.  It is less likely to work well for graphs with clusters
      (inducing subgraphs) of large diameter, e.g.  grid-like  graphs  derived
      from  Euclidean  data. So mcl in its canonical form is certainly not fit
      for boundary detection or image segmentation. I experimented with a mod-
      ified  mcl  and  boundary  detection in the thesis pointed to below (see
      REFERENCES). This was fun and not entirely unsuccesful,  but  not  some-
      thing to be pursued further.

      mcl  likes  undirected  input graphs best, and it really dislikes graphs
      with node pairs (i,j) for which an arc going from i to j is present  and
      the  counter-arc  from  j  to  i is absent. Try to make your input graph
      undirected.  Furthermore, mcl interprets edge weights in graphs as simi-
      larities. If you are used to working with dissimilarities, you will have
      to convert those to similarities using some conversion formula. The most
      important  thing  is  that  you feel confident that the similarities are
      reasonable, i.e. if X is similar to Y with weight 2, and X is similar to
      Z with weight 200, then this should mean that the similarity of Y (to X)
      is neglectible compared with the similarity of Z (to X).

      mcl is probably not suited for clustering tree graphs. This  is  because
      mcl  works  best  if there are multiple paths between different nodes in
      the natural clusters, but in tree graphs there is only one path  between
      any  pair of nodes. Trees are too sparse a structure for mcl to work on.

      mcl may well be suited for clustering lattices. It will  depend  on  the
      density  characteristics  of the lattice, and the conditions for success
      are the same as those for clustering graphs in general: The diameter  of
      the  natural  clusters  should not be too large.  NOTE when clustering a
      lattice, you have to cluster the underlying undirected  graph,  and  not
      the  directed  graph  that  represents the lattice itself. The reason is
      that one has to allow mcl (or any other cluster algorithm) to 'look back
      in  time',  so  to  speak. Clustering and directionality bite each other
      (long discussion omitted).

      mcl has a worst-case time complexity O(N*k^2), where N is the number  of
      nodes  in  the  graph, and k is the maximum number of neighbours tracked
      during computations. k depends on the -P  and  -S  options.  If  the  -S
      option  is  used  (which is the default setting) then k equals the value
      corresponding with this option. Typical values for k are  in  the  range
      500..1000.  The  average case is much better than the worst case though,
      as cluster structure itself has the  effect  of  helping  mcl's  pruning
      schemes, certainly if the diameter of natural clusters is not large.

  FILES
      There are currently no resource nor configuration files.  The mcl matrix
      format is described in the mcxio(5) section.

  ENVIRONMENT
      MCLXASCIIDIGITS
         When writing matrices in ascii format, mcl will use  the  environment
         variable  MCLXASCIIDIGITS  (if  present)  as the precision (number of
         digits) for printing the fractional part of values.

      MCLXIOVERBOSITY
         MCL and its sibling applications will  usually  report  about  matrix
         input/output  from/to  disk. The verbosity level can be regulated via
         MCLXIOVERBOSITY. These are the levels it can currently be set to.

          1  Silent but applications may alter this.
          2  Silent and applications can not alter this.
          4  Verbose but applications may alter this.
          8  Verbose and applications can not alter this (default).

      MCLXIOFORMAT
         MCL and its sibling applications will by default output  matrices  in
         ASCII  format  rather than binary format (cf. mcxio(5)).  The desired
         format can be controlled via the variable MCLXIOFORMAT. These are the
         levels it can currently be set to.

          1  Ascii format but applications may alter this.
          2  Ascii format and applications can not alter this (default).
          4  Binary format but applications may alter this.
          8  Binary format and applications can not alter this.

      MCLXASCIIFLAGS
         If matrices are output in ascii format, by default empty vectors will
         not be listed. Equivalently (during input time), vectors for which no
         listing  is  present are understood to be empty - note that the pres-
         ence of a vector is established using the domain information found in
         the  header part.  It is possible to enforce listing of empty vectors
         by setting bit '1' in the variable MCLXASCIIFLAGS.

  DIAGNOSTICS
      If mcl issues a diagnostic error, it will most  likely  be  because  the
      input  matrix  could not be parsed succesfully.  mcl tries to be helpful
      in describing the kind  of  parse  error.   The  mcl  matrix  format  is
      described in the mcxio(5) section.

  BUGS
      No   known   bugs  at  this  time.  Please  send  bug  reports  to  mcl-
      devel@micans.org.

  AUTHOR
      Stijn van Dongen.

  HISTORY/CREDITS
      The MCL algorithm was conceived in spring 1996 by  the  present  author.
      The  first  implementation of the MCL algorithm followed that spring and
      summer. It was written in Perl and proved the  viability  of  the  algo-
      rithm.  The implementation described here began its life in autumn 1997.
      The first versions of the vital matrix library were designed jointly  by
      Stijn  van  Dongen  and Annius Groenink in the period Oktober 1997 - May
      1999. The efficient matrix-vector multiplication routine was written  by
      Annius.  This  routine  is  without significant changes still one of the
      cornerstones of this MCL implementation.

      Since May 1999 all MCL libraries have seen much development and redesign
      by  the  present author. Matrix-matrix multiplication has been rewritten
      several times to take full advantage of the sparseness properties of the
      stochastic matrices brought forth by the MCL algorithm. This mostly con-
      cerns the issue of pruning - removal of small elements in  a  stochastic
      column in order to keep matrices sparse.

      Very instructive was that around April 2001 Rob Koopman pointed out that
      selecting the k largest elements out of a collection of n is  best  done
      using  a  min-heap.  This  was  the key to the second major rewrite (now
      counting three) of the MCL pruning schemes,  resulting  in  much  faster
      code,  generally  producing  a more accurate computation of the MCL pro-
      cess.

      In May 2001 Anton Enright initiated the parallellization of the mcl code
      and  threaded  inflation.  From  this example, Stijn threaded expansion.
      This was great, as the MCL data structures and operands  (normal  matrix
      multiplication  and  Hadamard multiplication) just beg for parallelliza-
      tion.

      In Jan 2003 the 03-010 release introduced support for  sparsely  enumer-
      ated  (i.e.  indices  need  not  be sequential) graphs and matrices, the
      result of a major overhaul of the matrix library and most higher layers.
      Conceptually,  the  library  now  sees matrices as infinite quadrants of
      which only finite subsections happen to have nonzero entries.

      Joost van Baal set up the mcl CVS  tree  and  packaged  mcl  for  Debian
      GNU/Linux.  He  completely  autotooled  the  sources, so much so that at
      first I found it hard to find them back  amidst  bootstrap,  aclocal.m4,
      depcomp, and other beauties.

      Jan  van der Steen shared his elegant mempool code. Philip Lijnzaad gave
      useful comments.  Philip,  Shawn  Hoon,  Abel  Ureta-Vidal,  and  Martin
      Mokrejs sent helpful bug reports.

      Abel  Ureta-Vidal  and  Dinakarpandian  Deendayal  commented on and con-
      tributed to mcxdeblast and mcxassemble.

      Tim Hughes contributed several good bug reports for mcxassemble,  mcxde-
      blast and zoem (a workhorse for clmformat).

  SEE ALSO
      mclfaq(7) - Frequently Asked Questions.

      mcxio(5) - a description of the mcl matrix format.

      There  are  many more utilities. Consult mclfamily(7) for an overview of
      and links to all the documentation and the utilities in the mcl  family.

      mcl  development  is discussed on mcl-devel@lists.micans.org, (subscrib-
      tion) information is at  https://lists.micans.org:446/listinfo/mcl-devel
      ,  this  list is archived at https://lists.micans.org:446/pipermail/mcl-
      devel/.

      mcl's home at http://micans.org/mcl/.

  REFERENCES
      Stijn van Dongen, Graph Clustering by Flow Simulation.  PhD thesis, Uni-
      versity of Utrecht, May 2000.
      http://www.library.uu.nl/digiarchief/dip/diss/1895620/inhoud.htm

      Stijn van Dongen. A cluster algorithm for graphs.  Technical Report INS-
      R0010, National Research Institute for Mathematics and Computer  Science
      in the Netherlands, Amsterdam, May 2000.
      http://www.cwi.nl/ftp/CWIreports/INS/INS-R0010.ps.Z

      Stijn van Dongen. A stochastic uncoupling process for graphs.  Technical
      Report INS-R0011, National Research Institute for Mathematics  and  Com-
      puter Science in the Netherlands, Amsterdam, May 2000.
      http://www.cwi.nl/ftp/CWIreports/INS/INS-R0011.ps.Z

      Stijn  van  Dongen. Performance criteria for graph clustering and Markov
      cluster  experiments.  Technical  Report  INS-R0012,  National  Research
      Institute  for  Mathematics  and  Computer  Science  in the Netherlands,
      Amsterdam, May 2000.
      http://www.cwi.nl/ftp/CWIreports/INS/INS-R0012.ps.Z

      Enright A.J., Van Dongen S., Ouzounis C.A.  An efficient  algorithm  for
      large-scale  detection  of  protein  families,  Nucleic  Acids  Research
      30(7):1575-1584 (2002).

  NOTES
      This page was generated from ZOEM manual macros, http://micans.org/zoem.
      Both  html  and  roff  pages can be created from the same source without
      having to bother with all the usual conversion problems,  while  keeping
      some level of sophistication in the typesetting.



  mcl 1.005, 05-118                 28 Apr 2005                           mcl(1)
