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arXiv · 2402.03653

Agent-Based Triangle Counting: Unlocking Truss Decomposition, Triangle Centrality, and Local Clustering Coefficient

Prabhat Kumar Chand·Apurba Das·Anisur Rahaman Molla
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Abstract

In this paper, we study the problem of \emph{triangle counting} in an arbitrary anonymous graph $G$ with $n$ nodes and $m$ edges using the \emph{mobile-agent model}. Our triangle-counting method serves as a building block for solving related problems such as truss decomposition, triangle centrality, and local clustering coefficient computation. The agents operate synchronously, have distinct identifiers and limited memory, and communicate only when co-located. Starting from an arbitrary placement of $n$ agents, we first obtain a dispersed configuration, elect a leader, construct a spanning tree, and determine the maximum degree $Δ$ and maximum agent identifier $λ$. A BFS tree is constructed separately, which is needed for repeated global communication. Using this setup, the agents enumerate triangles and compute node- and edge-level triangle information, which is subsequently used for truss and centrality computations. We also complement the theoretical analysis with simulation-based evaluations on representative graph instances. Overall, our results establish a mobile-agent-based framework for these fundamental graph analytics problems in anonymous networks.

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Prabhat Kumar Chand, Apurba Das, Anisur Rahaman Molla. 2026-09-12. Agent-Based Triangle Counting: Unlocking Truss Decomposition, Triangle Centrality, and Local Clustering Coefficient. https://arxiv.org/abs/2402.03653

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