[Paper Review] The relative importance of structure and dynamics on node influence in reversible spreading processes

Junyi Qu, Ming Tang+2 more|arXiv (Cornell University)|May 21, 2021

Mathematical and Theoretical Epidemiology and Ecology Models1 references4 citations

TL;DR

This paper proposes a novel structure-dynamics combined centrality (NSRC) that integrates neighbors' outgoing edges (positive structural effect) and infection risks (negative dynamical effect) to improve identification of influential spreaders in reversible SIS-like spreading processes. The key finding is that slightly weakening the influence of neighbors' infection risks (b < a) significantly enhances ranking accuracy, with improvements up to 100% over baseline measures across real-world networks.

ABSTRACT

The reversible spreading processes with repeated infection widely exist in nature and human society, such as gonorrhea propagation and meme spreading. Identifying influential spreaders is an important issue in the reversible spreading dynamics on complex networks, which has been given much attention. Except for structural centrality, the nodes' dynamical states play a significant role in their spreading influence in the reversible spreading processes. By integrating the number of outgoing edges and infection risks of node's neighbors into structural centrality, a new measure for identifying influential spreaders is articulated which considers the relative importance of structure and dynamics on node influence. The number of outgoing edges and infection risks of neighbors represent the positive effect of the local structural characteristic and the negative effect of the dynamical states of nodes in identifying influential spreaders, respectively. We find that an appropriate combination of these two characteristics can greatly improve the accuracy of the proposed measure in identifying the most influential spreaders. Notably, compared with the positive effect of the local structural characteristic, slightly weakening the negative effect of dynamical states of nodes can make the proposed measure play the best performance. Quantitatively understanding the relative importance of structure and dynamics on node influence provides a significant insight into identifying influential nodes in the reversible spreading processes.

Motivation & Objective

• To understand the relative importance of network structure and node dynamics in determining node influence during reversible spreading processes.
• To address the limitation of structural centrality alone in accurately identifying influential spreaders in complex networks.
• To develop a hybrid measure that integrates both local structural features and dynamic states of neighbors for improved influence ranking.
• To quantify the optimal balance between structural and dynamical factors in influence estimation.

Proposed method

• Proposes a new centrality index, NSRC, which combines the number of outgoing edges of neighbors (positive structural effect) and their infection risks (negative dynamical effect) using weighted parameters a and b.
• Uses a single-node control model to evaluate node influence in SIS dynamics, simulating spreading processes at varying transmission rates λ.
• Employs a weighted combination of neighbors' degree (outgoing edges) and their infection probabilities to compute the NSRC score for each node.
• Optimizes the weight parameters a and b through extensive simulations on eight real-world networks to maximize ranking accuracy.
• Compares NSRC performance against benchmark measures like degree centrality and NDIC (neighbors' degree-based index) using improved ratio η as a metric.
• Analyzes the impact of transmission rate λ on ranking accuracy, using values 1–3 times the epidemic threshold to ensure distinguishable influence.

Figure 1: Illustration of calculating the NSRC. The decimal number labeled to the node number is the probability of being in the infected state. The NSRC of node 1 is calculated as $C(1)=k_{1}+a(k_{2}^{out}+k_{3}^{out}+k_{4}^{out}+k_{5}^{out})-b(k_{2}^{out}\rho_{2}+k_{3}^{out}\rho_{3}+k_{4}^{out}\rh

Experimental results

Research questions

• RQ1 How do the structural characteristics of neighbors (e.g., number of outgoing edges) affect a node's spreading influence in reversible processes?
• RQ2 To what extent do the dynamical states of neighbors (e.g., infection risk) reduce a node’s spreading influence?
• RQ3 What is the optimal balance between structural and dynamical factors in identifying influential spreaders?
• RQ4 Can integrating both structural and dynamic features significantly improve influence ranking accuracy compared to structural centrality alone?
• RQ5 How does the relative weighting of structural vs. dynamical effects impact the performance of the proposed centrality measure?

Key findings

• The proposed NSRC centrality significantly improves influence ranking accuracy over baseline measures like degree centrality and NDIC, with improvements reaching up to 100% in some real-world networks.
• When the weight of neighbors' infection risks (b) is slightly less than the weight of their outgoing edges (a), the NSRC achieves optimal performance, indicating that dynamical effects should be moderately downweighted.
• The improved ratio η of NSRC over NDIC reaches approximately 80% in Netsci, Router, and Blog networks, and 10–30% in the remaining five networks across various transmission rates.
• The number of outgoing edges of neighbors is a more accurate indicator of local structural importance than their degree, enhancing the precision of influence estimation.
• The NSRC maintains high accuracy across different transmission rates (λ = 1–3 times the epidemic threshold), demonstrating robustness in diverse spreading conditions.
• The echo chamber effect—where common neighbors amplify spreading—slightly promotes spreading, justifying the need to moderately weaken the negative impact of infection risks.

Figure 2: The imprecision of NSRC as a function of $a$ and $b$ in eight real-world networks for $p=5\%$ . The real-world networks are Nstsci (a), Hamster (b), Router (c), Blog (d), CA_Hep (e), Email (f), PGP (g), Astro (h).