Fast Algorithms for Indices of Nested Split Graphs Approximating Real Complex Networks

TL;DR

This paper introduces a simulated annealing-based method to approximate real complex networks with nested split graphs, enabling efficient computation of various graph indices across diverse application domains.

Contribution

It develops a novel approach combining simulated annealing and geometrical properties of nested split graphs for fast approximation and index computation of complex networks.

Findings

Effective approximation of real networks with nested split graphs.

Significant reduction in computation time for graph indices.

Successful application across social, communication, linguistic, and chemical networks.

Abstract

We present a method based on simulated annealing to obtain a nested split graph that approximates a real complex graph. This is used to compute a number of graph indices using very efficient algorithms that we develop, leveraging the geometrical properties of nested split graphs. Practical results are given for six graphs from such diverse areas as social networks, communication networks, word associations, and molecular chemistry. We present a critical analysis of the appropriate perturbation schemes that search the whole space of nested split graphs and the distance functions that gauge the dissimilarity between two graphs.