Growing Small-World Networks Generated by Attaching to Edges

TL;DR

This paper presents a minimal model for growing small-world networks by attaching to edges, resulting in a plane graph with exponential degree distribution and high clustering, closely matching real-world networks.

Contribution

It introduces a new edge-attachment model for small-world networks, providing analytical and numerical insights into degree distribution, clustering, and path length growth.

Findings

Degree distribution decays exponentially with degree

Average clustering coefficient approximately 0.648

Average path length grows slightly slower than logarithmic with network size

Abstract

We introduce a minimal model of small-world growing network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially with degree and average clustering coefficient $C={3/2}ln3-1\approx 0.6479$, which are in good agreement with the numerical simulations. We also prove that the increasing tendency of average path length of the considered network is a little slower than the logarithm of the network order $N$.