16 May 2014
**clm info**
14-137

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.

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

**clm info**
**[-o** fname (*write to file fname*)

**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.

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

shared_defopt{-tf}

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.

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

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

Stijn van Dongen.

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

[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