8 Mar 2012
**mcx erdos**
12-068

mcx erdos — compute shortest paths in a graph

**mcx erdos** [options]

mcxerdos is not in actual fact a program. This manual
page documents the behaviour and options of the mcx program when
invoked in mode *erdos*. The options **-h**, **--apropos**,
**--version**, **-set**, **--nop**, **-progress** *<num>*
are accessible
in all **mcx** modes. They are described
in the mcx manual page.

**mcx erdos**
**[-query** <fname> (*query input stream*)**]**
**[-abc** <fname> (*specify label input*)**]**
**[-imx** <fname> (*specify matrix input*)**]**
**[-tab** <fname> (*use tab file*)**]**
**[-o** <fname> (*output file name*)**]**
**[--is-directed** (*input graph is directed*)**]**
**[--is-undirected** (*input graph is directed*)**]**
**[-write-path** <fname> (*path matrix file*)**]**
**[-write-step** <fname> (*step matrix file*)**]**
**[-h** (*print synopsis, exit*)**]**
**[--apropos** (*print synopsis, exit*)**]**
**[--version** (*print version, exit*)**]**

**mcx erdos** computes shortest paths in graphs.
It can read a graph either in label format with **-abc**
or in native format with **-imx**.
It reads pairs of node indices from an input stream, and for
each pair outputs a data structure describing the full
set of shortest paths between the two nodes.
Edge weights are not taken into account, so an
edge always represents a unit step size between two nodes
irrespective of its weight. A mode to compute shortest paths while taking into
account edge weights will be implemented later as **mcx dijkstra**.

Note that the full set of shortest paths between two nodes in
a graph can be described as a directed acyclic graph (DAG),
and this is how **mcx erdos** operates. It is easy to construct
graphs and node pairs for which the number of shortest paths
between the two nodes becomes exponential in the size of
the graph, whereas the lattice description is always
garantueed to map to a subset of the graph edge set.

By default it is assumed that the input graph should be treated as
undirected. To this end a transformation step is applied to ensure that the
graph in memory is undirected. It is possible to compute shortest
paths in directed graphs by using **--is-directed**, and
it is possible to omit the transformation step by using **--is-undirected**.
If the latter is specified while the input graph is in native format and in
fact directed, results will be erroneous. This could in theory be mitigated
by checking that the input graph is undirected. However, the reason to use
**--is-undirected** is simply to increase speed of operation, whereas
such a check would be equally expensive as the transformation step that is
omitted with **--is-undirected**.

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 using the
**-abc** option.
Refer to mcxio for a description of these two input formats.
By default **mcx erdos** reads from STDIN *and expects matrix format*.
To specify label input from STDIN use **-abc** **-**.

The name for the file from which queries are read.
A query consists of two white-space separated node indices
or two white-space separated labels. Labels can only be used
if either **-abc** or **-tab** is specified.

The file name for input that is in label format.

The file name for input that is in mcl native matrix format.

The name of the file to write output to.

This option causes the output to be printed with the labels
found in the tab file.
With **-abc** this option will, additionally, construct
a graph only on the labels found in the tab file.
If this option is used in conjunction with **-imx** the
tab domain and the matrix domain are required to be identical.

The input graph is not transformed and assumed to be directed. Shortest paths are computed taking this into account.

The input graph is not transformed and assumed to be undirected. Shortest paths are computed on the assumption that the input is undirected. Use this option only if you are sure the input is undirected and need to have faster execution.

The path matrix enumerates the nodes that take part in all shortest paths. The first list contains those nodes that lie at distance 1 of the source node, the second list contains nodes lying at distance 2, and so on. The step matrix contains all the edges that make up the lattice of shortest paths between the two query nodes.

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