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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.