9 Oct 2022 clm info 22-282

1.
NAME
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SYNOPSIS
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DESCRIPTION
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OPTIONS
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AUTHOR
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SEE ALSO
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REFERENCES

## NAME

clm info — compute performance measures for graphs and clusterings.

clminfo is not in actual fact a program. This manual page documents the behaviour and options of the clm program when invoked in mode info. The options -h, --apropos, --version, -set, --nop are accessible in all clm modes. They are described in the clm manual page.

## SYNOPSIS

clm info [options] <graph file> <cluster file> <cluster file>*

clm info [-o fname (write to file fname)] [-pi f (apply inflation beforehand)] [-tf spec (apply tf-spec to input matrix)] [-cl-tree fname (expect file with nested clusterings)] [-cat-max num (do at most num tree levels)] [-cl-ceil <num> (skip clusters of size exceeding <num>)] [--node-self-measures (dump measure for native cluster)] [--node-all-measures (dump measure for incident cluster)] [-h (print synopsis, exit)] [--apropos (print synopsis, exit)] [--version (print version, exit)] <matrix file> <cluster file> <cluster file>*

## DESCRIPTION

clm info computes several numbers indicative for the efficiency with with a clustering captures the edge mass of a given graph. Use it in conjunction with clm dist to determine which clusterings you accept. See the EXAMPLES section in clm dist for an example of clm dist and clm info (and clm meet) usage. Output can be generated for multiple clusterings at the same time.

The efficiency factor is described in [1] (see the REFERENCES section). It tries to balance the dual aims of capturing a lot of edges or edge weights and keeping the cluster footprint or area fraction small. The efficiency number has several appealing mathematical properties, cf. [1]. It is related to, but not derivable from, the second and third numbers, the mass fraction and the area fraction.

The mass fraction is defined as follows. Let e be an edge of the graph. The clustering captures e if the two nodes associated with e are in the same cluster. Now the mass fraction is the joint weight of all captured edges divided by the joint weight of all edges in the input graph.

The area fraction is roughly the sum of the squares of all cluster sizes for all clusters in the clustering, divided by the square of the number of nodes in the graph. It says roughly, because the actual formula uses the quantity N*(N-1) wherever it says square (of N) above. A low/high area fraction indicates a fine-grained/coarse clustering.

## OPTIONS

-o fname (output file name)
-pi f (apply inflation beforehand)

Apply inflation to the graph matrix and compute the performance measures for the result.

-tf <tf-spec> (transform input matrix values)

shared_defopt{-tf}

-cl-tree fname (expect file with nested clusterings (cone format))
-cl-ceil <num> (skip (nested) clusters of size exceeding <num>)

The specified file should contain a hierarchy of nested clusterings such as generated by mclcm. The output is then in a special format, undocumented but easy to understand. Its purpose is to help cherrypick a single clustering from a tree, in conjunction with the slightly experimental and undocumented program mlmfifofum.

The measure that is used is very slow to compute for large clusters, and generally it will be outside any interesting range (i.e. it will be small). Use -cl-ceil to skip clusters exceeding the specified size — clm info will directly proceed to subclusters if they exist.

-cat-max num (do at most num levels)

This only has effect when used with -cl-tree. clm info will start at the most fine-grained level, working upwards.

--node-all-measures (dump node-wise criteria for all incident clusters)
--node-self-measures (dump node-wise criteria for native cluster)

These options return a key-value based format, with the meaning of the keys as follows.

nm file name (redundant unless multiple cluster files are provided) ni node index ci cluster index nn number of neighbours of this node (constant for a give node) nc cluster size (constant for a given cluster) ef efficiency for this node/cluster combination em max-efficiency for this node/cluster combination mf mass fraction: percentage of edge weights for this node in this cluster ma total mass of edge weights for this node in this cluster xn number of neighbours of the node that are not in the cluster xc number of nodes in the cluster that are not a neighbour of the node ns number of neighbours of the node that are also in this cluster ti the maximum of the edge weights for neighbours of this node that are in this cluster to the maximum of the edge weights for neighbours of this node that are NOT in this cluster al (alien) 1 if the node is not native to the cluster, 0 if the node is native

## AUTHOR

Stijn van Dongen.

## SEE ALSO

mclfamily for an overview of all the documentation and the utilities in the mcl family.

## REFERENCES

[1] 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