A model for biological dynamic networks

Alessia Marigo; Benedetto Piccoli; Alessia Marigo; Benedetto Piccoli

doi:10.3934/nhm.2011.6.647

Networks and Heterogeneous Media

2011, Volume 6, Issue 4: 647-663. doi: 10.3934/nhm.2011.6.647

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A model for biological dynamic networks

Alessia Marigo ^{1
,},
Benedetto Piccoli ^{2
,}

1.
Department of Mathematical Sciences, Rutgers University - Camden, 311 N 5th Street, Camden, NJ 08102
2.
Department of Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University - Camden, 311 N 5th Street, Camden, NJ 08102

Received: 01 March 2011 Revised: 01 September 2011
Primary: 05C60, 92C42; Secondary: 05C80.

The main aim of this paper is to introduce a mathematical framework to study stochastically evolving networks. More precisely, we provide a common language and suitable tools to study systematically the probability distribution of topological characteristics, which, in turn, play a key role in applications, especially for biological networks. The latter is possible via suitable definition of a random network process and new results for graph isomorphism, which, under suitable generic assumptions, can be stated in terms of the graph walk matrix and computed in polynomial time.
- Dynamic networks,
- Biological networks,
- Isomorphic graphs
Citation: Alessia Marigo, Benedetto Piccoli. A model for biological dynamic networks[J]. Networks and Heterogeneous Media, 2011, 6(4): 647-663. doi: 10.3934/nhm.2011.6.647

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Abstract

The main aim of this paper is to introduce a mathematical framework to study stochastically evolving networks. More precisely, we provide a common language and suitable tools to study systematically the probability distribution of topological characteristics, which, in turn, play a key role in applications, especially for biological networks. The latter is possible via suitable definition of a random network process and new results for graph isomorphism, which, under suitable generic assumptions, can be stated in terms of the graph walk matrix and computed in polynomial time.

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