Does mathematica have any measures of bilateral distance in a

*To*: mathgroup at smc.vnet.net*Subject*: [mg131381] Does mathematica have any measures of bilateral distance in a*From*: Jesse Perla <jesseperla at gmail.com>*Date*: Wed, 17 Jul 2013 01:48:23 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Given a directed, weighted, graph with a particular number of connections between each node. For example represented by the matrix: A = {{0,1,1}, {5, 0, 1}, {1, 3, 0}} Is there any measure to determine the relative strength of the connection between nodes in the graph (which includes the flow between nodes)? Obviously I can use things like eigenvector centrality to see the relative importance of a particular node as a whole, but what about bilateral measures? Here I would want something asymmetric. i.e. node 3 flows into 1 both directly and indirectly, but not much flows from node 1 into 3. If mathematica doesn't have such an algorithm, does anyone know the name of a good algorithm (hopefully using spectral graph theory) to calculate some sort of measure? Bonus points if it allows self connections (e.g. A = {{8,1,1}, {5, 2, 1}, {1, 3, 1}})