mcxrand(1) USER COMMANDS mcxrand(1)
NAME
mcxrand - random shuffling, removal, addition, and perturbation of edges of graphs
SYNOPSIS
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)] [-noise-radius <num> (maximum spread to add noise with)] [-noise-sdev <num>
(noise standard deviation)] [-noise-range <num> (noise range factor)] [-edge-min <num> (absolute edge weight minimum)] [-edge-max <num>
(absolute edge weight maximum)] [-new-g-mean <num> (mean for new edges (Gaussian))] [-new-g-sdev <num> (standard deviation for new edges
(Gaussian))] [-new-g-radius <num> (maximum spread for new edges (Gaussian))] [-new-g-min <num> (lower bound selection (Gaussian))] [-new-g-
max <num> (upper bound selection (Gaussian))] [-skew <num> (skew towards min or max)] [-h (print synopsis, exit)] [--apropos (print synop-
sis, exit)] [--version (print version, exit)]
DESCRIPTION
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 prepro-
cessing the label input with mcxload(1), i.e.
mcxload -abc <label-file> | mcxrand [options]
Refer to mcxio(5) 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 direc-
tion 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 com-
bined 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.
OPTIONS
-imx <fname> (input matrix)
The file name for input. STDIN is assumed if neither -imx nor -gen num is specified.
-o <fname> (output matrix to <fname>)
The file to write the transformed matrix to.
--write-binary (write output in binary format)
Write the output matrix in native binary format.
-shuffle <num> (shuffle edge pair <num> times)
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 dif-
ferent. 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.
-pa <N>/<m> (preferential attachment)
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 propor-
tional 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 <num> (remove <num> edges)
Remove this many edges from the input graph.
-add <num> (add <num> edges not yet present)
Create this many new edges.
-gen <num> (node number)
Use in conjunction with -add to generate a random graph on <num> nodes.
-noise-radius <num> (maximum spread to add noise with)
-noise-sdev <num> (standard deviation)
-noise-range <fac> (number of standard deviations allowed)
See the discussion in DESCRIPTION.
-edge-min <num> (global edge weight minimum)
-edge-max <num> (global edge weight maximum)
See the discussion in DESCRIPTION.
-skew <num> (skew towards min or max)
See the discussion in DESCRIPTION.
-new-g-mean <num> (mean to generate new edges with)
-new-g-sdev <num> (standard deviation to generate new edges with)
-new-g-radius <num> (maximum spread to generate new edges with)
-new-g-min <num> (lower bound selection (Gaussian))
-new-g-max <num> (upper bound selection (Gaussian))
See the discussion in DESCRIPTION.
SEE ALSO
mcxio(5), and mclfamily(7) for an overview of all the documentation and the utilities in the mcl family.
mcxrand 12-068 8 Mar 2012 mcxrand(1)