Identifying Core-Periphery Structures in Networks via Artificial Ants

TL;DR

The proposed approach, inspired by the foraging behavior of ants, employs artificial pheromone trails to iteratively construct and refine solutions, thereby eliminating the need for arbitrary partitions that often constrain traditional methods.

Abstract

Core periphery structure represents a meso-scale structure in networks, characterized by a dense interconnection of core nodes and sparse connections among peripheral nodes. In this paper, we introduce an innovative approach for detecting core periphery structure, leveraging Artificial Ants. Core-periphery structures play a crucial role in elucidating network organization across various domains. The proposed approach, inspired by the foraging behavior of ants, employs artificial pheromone trails to iteratively construct and refine solutions, thereby eliminating the need for arbitrary partitions that often constrain traditional methods. Our method is applied to a diverse selection of real world networks including historical, literary, linguistic, sports, and animal social networks highlighting its adaptability and robustness. We systematically compare the performance of our approach against established core-periphery detection techniques, emphasizing differences in node classification between the core and periphery. Experimental results show that our method achieves superior flexibility and precision, offering marked improvements in the accuracy of core periphery structure detection.

Figures (5)

• Figure 1: Frobenius norm of the difference between the ideal core-periphery model and the normalized permuted adjacency matrices ($\|\Phi_{\text{ideal}} - \Phi_0\|_F$) as a function of parameters $\alpha$ and $\beta$ on Zachary's Karate Club graph for (a) $\rho = 0.1$, (b) $\rho = 0.3$, (c) $\rho = 0.5$, and (d) $\rho = 0.7$.
• Figure 2: Frobenius norm of the difference between the ideal core-periphery model and the normalized permuted adjacency matrices ($\|\Phi_{\text{ideal}} - \Phi_0\|_F$) as a function of parameters $\alpha$ and $\beta$ on Florentine Families graph for (a) $\rho = 0.1$, (b) $\rho = 0.3$, (c) $\rho = 0.5$, and (d) $\rho = 0.7$.
• Figure 3: Frobenius norm of the difference between the ideal core-periphery model and the normalized permuted adjacency matrices ($\|\Phi_{\text{ideal}} - \Phi_0\|_F$) as a function of parameters $\alpha$ and $\beta$ on Davis Southern Women graph for (a) $\rho = 0.1$, (b) $\rho = 0.3$, (c) $\rho = 0.5$, and (d) $\rho = 0.7$.
• Figure 4: Frobenius norm of the difference between the ideal core-periphery model and the normalized permuted adjacency matrices ($\|\Phi_{\text{ideal}} - \Phi_0\|_F$) as a function of parameters $\alpha$ and $\beta$ on the Krackhardt Kite graph for (a) $\rho = 0.1$, (b) $\rho = 0.3$, (c) $\rho = 0.5$, and (d) $\rho = 0.7$.
• Figure 5: Groundtruth adjacency matrices for the networks: (A) Word Adjacencies, (B) American College Football, (C) Dolphins, and (D) Books About US Politics. The adjacency matrices are ordered in decreasing order of core scores obtained using (a) our proposed method, (b) the Rossa method, (c) the Rombach method, and (d) the Boyd method.