Basic Cycle Ratio: Cost-Effective Ranking of Influential Spreaders from Local and Global Perspectives

TL;DR

The paper addresses identifying influential spreaders in networks by introducing Basic Cycle Ratio (BCR), which combines a node's participation in basic cycles (local structure) with its role in global cycle cohesion. BCR is computed via a three-step process using the basic cycle set, a cycle number matrix, and a node-specific ratio, enabling dual local-global ranking. Across six real-world networks, BCR outperforms classical centralities and cycle-based baselines in spreading efficacy, maintains cost-effectiveness, and demonstrates robustness to spanning-tree randomness. This approach provides a practical, scalable tool for effective information diffusion in social networks and related systems.

Abstract

Spreading processes are fundamental to complex networks. Identifying influential spreaders with dual local and global roles presents a crucial yet challenging task. To address this, our study proposes a novel method, the Basic Cycle Ratio (BCR), for assessing node importance. BCR leverages basic cycles and the cycle ratio to uniquely capture a node's local significance within its immediate neighborhood and its global role in maintaining network cohesion. We evaluated BCR on six diverse real-world social networks. Our method outperformed traditional centrality measures and other cycle-based approaches, proving more effective at selecting powerful spreaders and enhancing information diffusion. Besides, BCR offers a cost-effective and practical solution for social network applications.

Figures (8)

• Figure 1: Basic cycle ratios of nodes in an example network.
• Figure 2: Average Kendall’s tau ($\tau$) among the six indicators over six real-world networks. The values in each cell represent the average correlation between a pair of indicators, and the color intensity corresponds to the magnitude of $\tau$.
• Figure 3: Visualization of the top-50 ranked nodes identified by six indicators in the soc-hamsterster network. Across all plots, node importance is mapped to color (see legend) and size (larger indicates greater importance), while a fixed layout is maintained for consistent node positioning. (a) DC; (b) Coreness; (c) BC; (d) CR; (e) NC; (f) BCR.
• Figure 4: The frequency of nodes of each class for different indicators across six real networks. The $x$-axis shows the top node ranks, and the $y$-axis indicates the frequency of shared scores.
• Figure 5: Spreading ability of each indicator at $\beta$= 1.5$\beta_c$ for different sizes of the initial seed set $c$ (from the top 1% to 5%) over six empirical networks. The $x$-axis denotes the initial seed proportion ($c$), and the $y$-axis indicates the proportion of infected nodes ($R$) in the spreading.