mcx erdos(1)							  USER COMMANDS 						      mcx erdos(1)

  NAME
      mcx erdos - compute shortest paths in a graph

  SYNOPSIS
      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)]

  DESCRIPTION
      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 expo-
      nential 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(5) 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 -.

  OPTIONS
      -query <fname> (query input)
	The name for the file from which queries are read.  A query consists of two white-space separated node indices or  two	white-space  sepa-
	rated labels. Labels can only be used if either -abc or -tab is specified.

      -abc <fname> (label input)
	The file name for input that is in label format.

      -imx <fname> (input matrix)
	The file name for input that is in mcl native matrix format.

      -o <fname> (output file name)
	The name of the file to write output to.

      -tab <fname> (use tab file)
	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.

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

      --is-undirected (skip symmetrification step)
	The  input  graph  is not transformed and assumed to be undirected.  Shortest paths are computed on the assumption that the input is undi-
	rected. Use this option only if you are sure the input is undirected and need to have faster execution.

      -write-path <fname> (path matrix file)
      -write-step <fname> (step matrix file)
	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.

  SEE ALSO
      mcxio(5), and mclfamily(7) for an overview of all the documentation and the utilities in the mcl family.

  mcx erdos 12-068						      8 Mar 2012							mcx erdos(1)