Evolution of a Modified Binomial Random Graph by Agglomeration

Mihyun Kang, Angelica Pachon, Pablo M. Rodríguez*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Downloads (Pure)


In the classical Erdős–Rényi 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 Erdős-Rényi 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.

Original languageEnglish
Pages (from-to)509-535
Number of pages27
JournalJournal of Statistical Physics
Issue number3
Publication statusPublished - 15 Dec 2017
Externally publishedYes


  • Connectedness
  • Erdős–Rényi model
  • Inhomogeneous random graph
  • Phase transition
  • Random graph


Dive into the research topics of 'Evolution of a Modified Binomial Random Graph by Agglomeration'. Together they form a unique fingerprint.

Cite this