A simple and fast exact clustering algorithm defined for complex networks and based on the properties of primes

Abstract

In this paper a new clustering method based on primes is proposed. This method define a nodes cluster of any complex network, considering the nodes with same input/output number and same number of paths with equal length, so all the network nodes with analogous functions will be possible to identify. The clustering algorithm proposed, results very efficient because it is defined on simple computations with primes. For example, with our algorithm the analysis of a network with 500 nodes and 124750 connections is performed in 80 seconds on Pentium 4 with CPU 2Ghz and 1Gb ram.

Keywords: Complex network, clustering method, graph theory, unidirectional/bidirectional network, complete path.