A universal optimization framework based on cycle ranking for influence maximization in complex networks

TL;DR

The paper tackles influence maximization in complex networks, framing the problem as selecting a small influencer set to maximize diffusion under NP-hard constraints. It introduces CycRak, a cycle-ranking optimization framework that ranks basic cycles via a three-fold importance metric and selects influencer nodes from the most important cycles while enforcing non-adjacency. Across 13 networks (4 empirical and 9 synthetic), CycRak consistently outperforms four centrality-based benchmarks, achieving 1.5–3× higher diffusion, greater dispersibility, and substantially lower hub properties. The results highlight the underappreciated role of basic cycle structures in diffusion dynamics and suggest extensions to other cycle types and to directed/weighted networks, with available code at the provided GitHub repository.

Abstract

Influence maximization aims to identify a set of influential individuals, referred to as influencers, as information sources to maximize the spread of information within networks, constituting a vital combinatorial optimization problem with extensive practical applications and sustained interdisciplinary interest. Diverse approaches have been devised to efficiently address this issue, one of which involves selecting the influencers from a given centrality ranking. In this paper, we propose a novel optimization framework based on ranking basic cycles in networks, capable of selecting the influencers from diverse centrality measures. The experimental results demonstrate that, compared to directly selecting the top-k nodes from centrality sequences and other state-of-the-art optimization approaches, the new framework can expand the dissemination range by 1.5 to 3 times. Counterintuitively, it exhibits minimal hub property, with the average distance between influencers being only one-third of alternative approaches, regardless of the centrality metrics or network types. Our study not only paves the way for novel strategies in influence maximization but also underscores the unique potential of underappreciated cycle structures.

Figures (16)

• Figure 1: Visualization of the most important (in red) and least important (in dark brown) basic cycles in four empirical networks. Different communities within the networks are identified using the Louvain algorithm, distinguished by the colors of nodes and edges.
• Figure 2: Comparison of the influence with different percentages of influencers on four empirical networks. Each panel presents results for a specific centrality, with the network and centrality name indicated in its title. Each curve depicts the collective influence $F(\rho)$ of influencers selected by a particular optimization framework as a function of their percentage $\rho$. These results are captured under SIR model parameters $\gamma=1.25\beta_c$ and $\mu=1$, and each ($\rho$,$F(\rho)$) represents the average of 300 independent realizations.
• Figure 3: Performance improvement of CycRak relative to TopK with different percentages of influencers for four empirical networks. Here $\rho$ represents the percentage of influencers, and $R(\rho)$ indicates the factor by which CycRak's performance exceeds that of TopK. The black solid line denotes the influence of TopK, serving as the baseline, with each dashed line corresponding to a centrality.
• Figure 4: Comparison of the influence with different infection probabilities on four empirical networks. Each panel presents results for a specific centrality, with the network and centrality name indicated in its title. Each curve depicts the collective influence $F(\gamma)$ of the top-2% influencers selected by a particular optimization framework as a function of the infection probability $\gamma$. Here the x-axis is represented as the multiplier $\alpha \in [1.5,2.0]$ and $\gamma=\alpha \beta_c$. Each ($\gamma$, $F(\gamma)$) represents the average of 300 independent realizations, with $\mu=1$ held constant throughout.
• Figure 5: Performance improvement of CycRak over TopK at different infection probabilities for four empirical networks. Here, $\gamma$ represents the infection probability and $\gamma=\alpha \beta_c$, where $\alpha \in [1.5,2.0]$. $R(\rho)$ indicates the factor by which the influence of the top-2% influencers selected by CycRak exceeds that of TopK. The black solid line denotes the influence of TopK, serving as the baseline, with each dashed line corresponding to the results of CycRak in an empirical network, based on the centrality represented by the panel.