### 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 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 O ( Nn + Nn log( n)) 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).

Original language | English |
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Article number | 50006 |

Pages (from-to) | - |

Journal | Europhysics Letters |

Volume | 108 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Dec 2014 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)