Finding induced subgraphs in scale-free inhomogeneous random graphs

TL;DR

This paper presents a fast algorithm for finding specific induced subgraphs in inhomogeneous scale-free random graphs, leveraging their structure to achieve efficient detection in large networks.

Contribution

The authors introduce a novel $O(nk)$ time algorithm for induced subgraph detection in scale-free graphs, improving efficiency for large inhomogeneous networks.

Findings

Algorithm runs in $O(nk)$ time for small $k$

Effective in real-world data sets

Solves induced subgraph isomorphism efficiently

Abstract

We study the problem of finding a copy of a specific induced subgraph on inhomogeneous random graphs with infinite variance power-law degrees. We provide a fast algorithm that finds a copy of any connected graph $H$ on a fixed number of $k$ vertices as an induced subgraph in a random graph with $n$ vertices. By exploiting the scale-free graph structure, the algorithm runs in $O(n k)$ time for small values of $k$. As a corollary, this shows that the induced subgraph isomorphism problem can be solved in time $O(nk)$ for the inhomogeneous random graph. We test our algorithm on several real-world data sets.