| Issue |
EPL
Volume 108, Number 5, December 2014
|
|
|---|---|---|
| Article Number | 50006 | |
| Number of page(s) | 5 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/108/50006 | |
| Published online | 05 December 2014 | |
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
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