Community-detection cellular automata with local and long-range connectivity

We explore a community-detection cellular automata algorithm inspired by human heuristics, based on information diffusion and a non-linear processing phase with a dynamics inspired by human heuristics. The main point of the methods is that of furnishing different “views” of the clustering levels from an individual point of view. We apply the method to networks with local connectivity and long-range rewiring.

💡 Research Summary

The paper introduces a novel community‑detection algorithm that combines information diffusion with a non‑linear competition phase, both inspired by human heuristics, and implements the process as a cellular automaton (CA). The authors argue that traditional community‑detection methods rely on global graph metrics such as betweenness or modularity, which are impractical for massive, dynamic networks like the World Wide Web. In contrast, humans often make decisions with limited local information using heuristics such as “take the best”. The proposed model mirrors this behavior: each node is an autonomous agent that stores a probability vector S(i) representing its belief about belonging to each possible community.

Network construction: N nodes are organized into G groups, each containing C communities. Initially, nodes are linked locally with a K‑nearest‑neighbor scheme (periodic boundary conditions) forming a regular lattice within each community. With probability p_r a link is rewired; rewired links are placed either within the same community (probability p_c), within the same group but a different community (probability (1‑p_c)·p_g), or anywhere in the network (probability (1‑p_c)(1‑p_g)). This yields a three‑level hierarchy (node → community → group → whole network) that can be tuned from purely local to small‑world‑like structures.

Dynamics: The algorithm proceeds in discrete synchronous steps, each consisting of a diffusion phase followed by a competition phase.

1. Diffusion: The adjacency matrix A is row‑normalized to obtain a Markov communication matrix M (M_ij = A_ij / Σ_k A_ik). The state vector updates as
   S_i(t+½) = m·S_i(t) + (1‑m)·M·S_i(t) ,
   where m∈