Evolution of a Modified Binomial Random Graph by Agglomeration

Autor(es)

Kang, Mihyun ^[1] ; Pachon, Angelica ^[2] ; Rodriguez, Pablo M. ^[3]

Afiliação do(s) autor(es)

^[1] Graz Univ Technol, Inst Discrete Math, Steyrergasse 30, A-8010 Graz - Austria

^[2] Univ Turin, Dipartimento Matemat, Via Carlo Alberto 10, I-10123 Turin - Italy

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400 Ctr, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 170, n. 3, p. 509-535, FEB 2018.
• Citações Web of Science: 0

Resumo

In the classical ErdAs-R,nyi random graph G(n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the ErdAs-R,nyi random graph G(n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G(n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G(n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications. (AU)

• Processo FAPESP: 13/03898-8 - Modelagem estocástica da difusão de uma informação em sistemas interagentes
• Beneficiário: Pablo Martin Rodriguez
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/03868-7 - Comportamento assintótico de processos estocásticos em grafos e aplicações
• Beneficiário: Pablo Martin Rodriguez
• Linha de fomento: Bolsas no Exterior - Pesquisa