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Strongly clustered random graphs via triadic closure: An exactly solvable model.
Cirigliano, Lorenzo; Castellano, Claudio; Baxter, Gareth J; Timár, Gábor.
Afiliação
  • Cirigliano L; Dipartimento di Fisica Università "Sapienza", P. le A. Moro, 2, I-00185 Rome, Italy.
  • Castellano C; Centro Ricerche Enrico Fermi, Piazza del Viminale, 1, I-00184 Rome, Italy.
  • Baxter GJ; Centro Ricerche Enrico Fermi, Piazza del Viminale, 1, I-00184 Rome, Italy.
  • Timár G; Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, I-00185 Rome, Italy.
Phys Rev E ; 109(2-1): 024306, 2024 Feb.
Article em En | MEDLINE | ID: mdl-38491655
ABSTRACT
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static triadic closure (STC) model for clustered networks, whereby starting from an arbitrary fixed backbone network, each triad is closed independently with a given probability. Assuming a locally treelike backbone we derive exact expressions for the expected number of various small, loopy motifs (triangles, 4-loops, diamonds, and 4-cliques) as a function of moments of the backbone degree distribution. In this way we determine how transitivity and its suitably defined generalizations for higher-order motifs depend on the heterogeneity of the original network, revealing the existence of transitions due to the interplay between topologically inequivalent triads in the network. Furthermore, under reasonable assumptions for the moments of the backbone network, we establish approximate relationships between motif densities, which we test in a large dataset of real-world networks. We find a good agreement, indicating that STC is a realistic mechanism for the generation of clustered networks, while remaining simple enough to be amenable to analytical treatment.

Texto completo: 1 Bases de dados: MEDLINE Idioma: En Revista: Phys Rev E Ano de publicação: 2024 Tipo de documento: Article País de afiliação: Itália

Texto completo: 1 Bases de dados: MEDLINE Idioma: En Revista: Phys Rev E Ano de publicação: 2024 Tipo de documento: Article País de afiliação: Itália