Fingerprint for Network Topologies

Abstract

Abstract. A network's topology information can be given as an adjacency matrix. The bitmap of sorted adjacency matrix (BOSAM) is a network visualisation tool which can emphasise different network structures by just looking at reordered adjacent matrixes. A BOSAM picture resembles the shape of a flower and is characterised by a series of 'leaves'. Here we show and mathematically prove that for most networks, there is a self-similar relation between the envelope of the BOSAM leaves. This self-similar property allows us to use a single envelope to predict all other envelopes and therefore reconstruct the outline of a network's BOSAM picture. We analogise the BOSAM envelope to human's fingerprint as they share a number of common features, e.g. both are simple, easy to obtain, and strongly characteristic encoding essential information for identification.

Pixel-Oriented Visualization of Change in Social Networks

“…By mapping each data value onto one single pixel in theory the amount of data displayed is equal to the number of pixels. Pixel-oriented visualization has been applied by Guo et al [21] for the visualization of very large scale network matrices (BOSAM 7 ), but to the best of our knowledge it has not been tried on temporal and weighted networks yet.…”

AC power flow importance measures considering multi-element failures

“…In NWRank, relative weights are assigned to links based on the degree of the adjacent neighbors and their Betweenness Centrality instead of assigning the same weight to every link as assumed in PageRank[30]. Simpler metrics, such as the degree centrality, give the highest score of importance to the node with the largest number of neighbors[31,34]. The betweenness centrality is an indicator of a node's (or link's) centrality in a network from an approximate flow perspective.…”