[Paper Review] Identifying influential nodes in complex networks: Effective distance gravity model

Qiuyan Shang, Yong Deng+1 more|arXiv (Cornell University)|Nov 12, 2020

Complex Network Analysis Techniques49 references4 citations

TL;DR

This paper proposes an effective distance gravity model (EffG) that identifies influential nodes in complex networks by replacing traditional Euclidean distance with effective distance—derived from probabilistic path analysis—to better capture dynamic node interactions. The method fuses local and global network information, outperforming six existing methods in simulations using the SI model across eight real-world networks, demonstrating superior stability and correlation with actual information propagation dynamics.

ABSTRACT

The identification of important nodes in complex networks is an area of exciting growth due to its applications across various disciplines like disease controlling, community finding, data mining, network system controlling, just to name a few. Many measures have thus been proposed to date, and these measures are either based on the locality of nodes or the global nature of the network. These measures typically use distance based on the concept of traditional Euclidean Distance, which only focus on the local static geographic distance between nodes but ignore the interaction between nodes in real-world networks. However, a variety of factors should be considered for the purpose of identifying influential nodes, such as degree, edge, direction and weight. Some methods based on evidence theory have also been proposed. In this paper, we have proposed an original and novel gravity model with effective distance for identifying influential nodes based on information fusion and multi-level processing. Our method is able to comprehensively consider the global and local information of the complex network, and also utilize the effective distance to replace the Euclidean Distance. This allows us to fully consider the complex topological structure of the real network, as well as the dynamic interaction information between nodes. In order to validate the effectiveness of our proposed method, we have utilized the susceptible infected (SI) model to carry out a variety of simulations on eight different real-world networks using six existing well-known methods. The experimental results indicate the reasonableness and effectiveness of our proposed method.

Motivation & Objective

• To address the limitation of existing node influence measures that rely on static Euclidean distance and ignore dynamic interactions between nodes in real-world networks.
• To develop a method that integrates both local topological features and global network structure for more accurate influence assessment.
• To replace traditional distance metrics with effective distance—based on the probability of paths derived from adjacency matrices—to reflect real dynamic interactions in networks.
• To validate the proposed method's effectiveness in predicting information propagation using the susceptible-infected (SI) model across diverse real-world networks.
• To demonstrate that the proposed method achieves higher correlation with actual spreading dynamics than six well-known existing methods.

Proposed method

• The method replaces Euclidean distance in the gravity model with effective distance, which quantifies the likelihood of information flow between nodes based on network topology.
• Effective distance is computed using the adjacency matrix to estimate the most probable path between nodes, capturing dynamic interaction potential.
• The gravity model integrates node degree (local influence) and effective distance (global reachability) to compute a composite influence score.
• The influence score combines the mass of nodes (e.g., degree) and the effective distance between nodes, following a gravity-like formulation: F_ij = m_i * m_j / d_eff_ij.
• The method performs multi-level information fusion by combining local connectivity and global path probabilities to rank node influence.
• The model is evaluated using the SI model, where each node is initialized as an infected node and the final number of infected nodes is used as a ground truth for influence.

Experimental results

Research questions

• RQ1 How does replacing Euclidean distance with effective distance improve the identification of influential nodes in complex networks?
• RQ2 To what extent does the proposed effective distance gravity model (EffG) correlate with actual information propagation dynamics in real-world networks?
• RQ3 How does the performance of EffG compare to six established methods (e.g., DC, BC, CC, EC, PageRank, KS) in predicting influence spread across diverse network types?
• RQ4 Does the proposed model maintain stable and consistent performance across different network structures and spreading thresholds?
• RQ5 Can the effective distance metric better capture dynamic interactions between nodes than static geometric distance in influence propagation scenarios?

Key findings

• The proposed effective distance gravity model (EffG) achieved the highest Kendall’s tau correlation with the SI model’s final infection count in four real-world networks (Jazz, NS, Email, USAir), indicating strong alignment with actual spreading dynamics.
• In the Jazz network, EffG showed a consistently declining curve when plotting node ranking against final infected nodes, with minimal fluctuation, outperforming BC and EC which exhibited significant instability.
• On the Facebook network, EffG’s correlation with the SI model was second-highest when β > 0.9, and remained stable across varying spreading rates, while BC showed large fluctuations.
• In the USAir network, EffG and BC had lower tau values, but EffG maintained a more stable and reliable decline in influence ranking compared to BC’s erratic behavior.
• Across all eight tested networks, EffG demonstrated superior robustness and consistency, especially under varying spreading thresholds (β), with minimal performance degradation.
• The method outperformed traditional centrality measures like degree centrality (DC) and betweenness centrality (BC), which showed high sensitivity and instability in dynamic propagation scenarios.