16 May 2014
**mcxrand**
14-137

mcxrand — random shuffling, removal, addition, and perturbation of edges of graphs

**mcxrand** [options]

mcxrand -gen K -add N -new-g-mean f # random graph on K nodes, N edges
mcxrand -imx <name> -remove N -add N # remove then add edges
mcxrand -imx <name> -shuffle N # shuffle N edge pairs
mcxrand -imx <name> -noise-radius f # add noise to add weights

mcxrand -pa N/m # preferential attachment generation
**mcxrand**
**[-imx** <fname> (*input matrix*)**]**
**[-o** <fname> (*output matrix to <fname>*)**]**
**[--write-binary** (*write output in binary format*)**]**
**[-gen** <num> (*generate new graph*)**]**
**[-pa** <N>/<m> (*preferential attachment*)**]**
**[-remove** <num> (*remove <num> edges*)**]**
**[-add** <num> (*add <num> edges not yet present*)**]**
**[-shuffle** <num> (*shuffle edge pair <num> times*)**]**
**[-icl** <fname> (*shuffle nodes preserving cluster sizes*)**]**
**[-h** (*print synopsis, exit*)**]**
**[--apropos** (*print synopsis, exit*)**]**
**[--version** (*print version, exit*)**]**

This utility is a recent addition to the mcl suite and the schemes explained below will likely be evolved, simplified, and extended with future releases.

The **--shuffle**, **-gen** and **-pa** options can be deemend
stable and robust. The options that determine edge weight perturbation and
generation are likely to be subject to revision in the future.

The input graph/matrix, if specified with the **-imx** option,
has to be in mcl matrix/graph format.
You can use label input instead by preprocessing the label input
with mcxload, i.e.

mcxload -abc <label-file> | mcxrand [options]

Refer to mcxio for a description of these two input formats.
By default **mcxrand** reads from STDIN. Change this with the **-imx**
option.

**mcxrand** can randomly remove and add edges to a graph, or add gaussian noise
to the edge weights of a graph. It can also shuffle edge pairs while
preserving the degree sequence of the graph.
In *removal mode* (**-remove** *<num>*) and in
*addition mode* (**-add** *<num>*)
**mcxrand** enforces arc symmetry by only working with edges
*w(i,j)* where *i < j* and symmetrifying the result and adding any
loops that were present in the input graph just before the output stage.

In *perturbation mode* (**-noise-radius**, with no other mode specified)
the input can be any graph.

*Shuffle mode* (**-shuffle** *<num>*) requires an undirected graph
but will only fail when it picks an arc for which the arc in the reverse
direction is not present. This means it may or may not fail on directed
input depending on the random choices. It does not check equality of the two
arc weights and randomly picks one to represent the edge weight.

Edge removal, edge creation, and edge perturbation are applied in this order if both are specified. Edge shuffling presently cannot be combined with one of the previous modes.

A random graph can be generated with **-gen** *k*, which
specifies the number of nodes the graph should have. It is equivalent
with pasing (the file name of) an empty graph of the same dimensions as the argument
to **-imx**.

When adding (i.e. creating) edges, the default is to use the uniform
distribution for new edge weights ranging in some interval.
The default interval is [0,1] and can be modified using the
**-edge-min** *min* and **-edge-max** *max* options.
A Gaussian edge weight distribution can be obtained by specifying
**-new-g-mean** *num*. The standard deviation is by default
1.0 and can be altered with **-new-g-sdev** *num*.
Currently the edge weigths are generated within the interval
[*mean-radius*, *mean+radius*] where *radius* is specified
with **-new-g-radius**. They are further selected to
lie within the interval *[L,R]* if and only if
**-new-g-min** *L* and **-new-g-max** *R* have
been specified.

For both uniform and Gaussian edge creation the edge weights
can be skewed towards either side of the distribution with
**-skew** *c*. Skewing is applied by mapping
the edge weights to the interval [0,1], applying
the function *x^c*, and remapping the resulting number.
For values *c<1* this skews the edge weights towards
the right bound and for values *c>1* this skews the edge
weights towards the left bound.
This is a rather crude approach that will likely be
changed in the future.

Edge weights can be perturbed by specifying **-noise-radius** *radius*.
This sets the maximum perturbation allowed. Noise is generated with
a standard deviation that is by default set to 0.5 and can be altered
using **-noise-sdev** *num*.
Values are generated in the interval *[-fac*sdev, fac*sdev]*
where *fac* is set with **-noise-range** *fac*.
This interval is mapped to the interval *[-radius, radius]* before
the resulting value is added to the actual edge weight.
This becomes the new value. If an interval *[L,R]* is explicitly
specified using **-edge-min** *L* and **-edge-max** *R*
then the new value will be accepted only if it lies within the interval,
otherwise the edge will not be perturbed.

The file name for input. STDIN is assumed if neither
**-imx** nor **-gen** *num* is specified.

The file to write the transformed matrix to.

Write the output matrix in native binary format.

Shuffle edge pair <num> times. An edge shuffle
acts on two randomly chosen edges
edges *w(a,b)* and *w(c,d)* where all the nodes must
be different. If either none of the edges in *w(a,c)*, *w(b,d)*
or none of the edges in *w(a,d)*, *w(b,c)* exists
the original two edges are removed and is replaced
by an edge pair for which both edges did not exist before.

Use this option to generate a random clustering with the exact same cluster size distribution as the input clustering.

This generates a random graph using preferential attachment.
In this model new nodes are sequentially added to a graph.
Each new node is connected with *<m>* of the existing
nodes (including nodes previously added), where the likelihood
of picking an existing node is proportional to the edge
degree of that node. During construction multiple edges between
two nodes are allowed (each with weight one), and these are collapsed by adding
their weights before output.

Remove this many edges from the input graph.

Create this many new edges.

Use in conjunction with **-add** to generate
a random graph on *<num>* nodes.

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