Identifying sparse and dense sub-graphs in large graphs with a fast algorithm
Data Structures and Algorithms
2015-06-22 v1 Social and Information Networks
Abstract
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 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 O(N n). Relaxing the problem to complete sub-graphs, the same performance is obtained with a single background. The worst case complexity for the single background is O(n log(n)).
Cite
@article{arxiv.1409.5000,
title = {Identifying sparse and dense sub-graphs in large graphs with a fast algorithm},
author = {Vincenzo Fioriti and Marta Chinnici},
journal= {arXiv preprint arXiv:1409.5000},
year = {2015}
}