Local rewiring algorithms to increase clustering and grow a small world

TL;DR

This paper introduces local edge-rewiring algorithms that increase clustering in existing networks without adding or removing edges, transforming them into small-world networks with high clustering and low path length.

Contribution

The authors present novel local rewiring algorithms that enhance clustering in networks while preserving other properties, enabling organic formation of small-world structures.

Findings

Algorithms significantly increase clustering coefficient.

Networks achieve small-world characteristics with high clustering and low path length.

Rewiring preserves original network properties while enhancing clustering.

Abstract

Many real-world networks have high clustering among vertices: vertices that share neighbors are often also directly connected to each other. A network's clustering can be a useful indicator of its connectedness and community structure. Algorithms for generating networks with high clustering have been developed, but typically rely on adding or removing edges and nodes, sometimes from a completely empty network. Here, we introduce algorithms that create a highly clustered network by starting with an existing network and rearranging edges, without adding or removing them; these algorithms can preserve other network properties even as the clustering increases. They rely on local rewiring rules, in which a single edge changes one of its vertices in a way that is guaranteed to increase clustering. This greedy step can be applied iteratively to transform a random network into a form with much higher clustering. Additionally, the algorithms presented grow a network's clustering faster than they increase its path length, meaning that network enters a regime of comparatively high clustering and low path length: a small world. These algorithms may be a basis for how real-world networks rearrange themselves organically to achieve or maintain high clustering and small-world structure.