Identifying sparse and dense sub-graphs in large graphs with a fast algorithm
ENEA CR Casaccia - Via Anguillarese 301, 00123 Rome, Italy
Received: 27 September 2014
Accepted: 19 November 2014
Identifying the nodes of small sub-graphs with no a priori information is a hard problem. In this work, we want to find each node of a sparse sub-graph embedded in both dynamic and static background graphs, of larger average degree. We show that by exploiting the summability over several background realizations of the Estrada-Benzi communicability and the Krylov approximation of the matrix exponential, it is possible to recover the sub-graph with a fast algorithm with computational complexity in the worst case, where n is the number of nodes and N is the number of backgrounds. Relaxing the problem to complete sub-graphs, the same performance is obtained with a single background, with a best case complexity O(n).
PACS: 02.10.Ox – Combinatorics; graph theory / 89.75.Hc – Networks and genealogical trees / 02.70.Hm – Spectral methods
© EPLA, 2014