Models of on-line social networks

TL;DR

This paper introduces the Iterated Local Transitivity (ILT) model for online social networks, capturing key properties like densification, clustering, and community structure, supported by theoretical analysis and experimental validation.

Contribution

The paper proposes a new deterministic ILT model for OSNs that replicates observed network properties and analyzes its structural and spectral characteristics.

Findings

ILT model satisfies densification power law

Graphs exhibit poor expansion properties

Spectral gap bounds indicate community structure

Abstract

We present a deterministic model for on-line social networks (OSNs) based on transitivity and local knowledge in social interactions. In the Iterated Local Transitivity (ILT) model, at each time-step and for every existing node $x$, a new node appears which joins to the closed neighbour set of $x.$ The ILT model provably satisfies a number of both local and global properties that were observed in OSNs and other real-world complex networks, such as a densification power law, decreasing average distance, and higher clustering than in random graphs with the same average degree. Experimental studies of social networks demonstrate poor expansion properties as a consequence of the existence of communities with low number of inter-community edges. Bounds on the spectral gap for both the adjacency and normalized Laplacian matrices are proved for graphs arising from the ILT model, indicating such bad expansion properties. The cop and domination number are shown to remain the same as the graph from the initial time-step $G_0$, and the automorphism group of $G_0$ is a subgroup of the automorphism group of graphs generated at all later time-steps. A randomized version of the ILT model is presented, which exhibits a tuneable densification power law exponent, and maintains several properties of the deterministic model.