Ranking the spreading influence in complex networks (1408.4649v1)

Abstract: Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a target node and the node set with the highest $k$-core value, we present an improved method to generate the ranking list to evaluate the node spreading influence. Comparing with the epidemic process results for four real networks and the Barab\'{a}si-Albert network, the parameterless method could identify the node spreading influence more accurately than the ones generated by the degree $k$, closeness centrality, $k$-shell and mixed degree decomposition methods. This work would be helpful for deeply understanding the node importance of a network.

• The paper introduces a novel parameterless method refining the k-shell decomposition by incorporating node distance to the network core for more accurate influence ranking.
• Performance evaluation across empirical networks shows the improved method significantly outperforms traditional approaches, particularly when spreading rates exceed the epidemiological threshold.
• This enhanced ranking capability provides a valuable tool for identifying key influencers, aiding strategies in network resilience, information dissemination, and infection control.

Ranking the Spreading Influence in Complex Networks: An Expert Analysis

This paper presents an advanced methodology for ranking node influence in complex networks, aimed at improving our understanding and management of spreading processes such as epidemics, information diffusion, and cascading failures. Traditional approaches, notably the $k$-shell decomposition, are critiqued for their limitations, and a novel parameterless method is introduced that demonstrates superior performance in various network contexts.

Methodology

The primary innovation in this paper is an improved $k$-shell method that takes into account not only the core number of a node (i.e., the $k$-core value) but also the shortest distance to the network core—a set of nodes with the highest $k$-core values. Their new metric, denoted as $\theta(i|k_s)$, is designed to generate a more precise ranking list of spreading influence across a network. The method calculates influence by pairing the $k$-core value of nodes with their proximities to the most influential nodes, providing a refined perspective on node importance.

Performance Evaluation

The paper evaluates the efficacy of this improved method in four empirical networks—Email, Peer-to-Peer (P2P), Pretty-Good-Privacy (PGP), and Autonomous Systems (AS) networks—using metrics like the Kendall's tau coefficient to compare the rank correlation between various metrics and simulation-grounded SIR model results. This assessment revealed that the novel method significantly outperforms traditional approaches, such as degree centrality, closeness centrality, $k$-shell decomposition, and the Mixed Degree Decomposition (MDD) method, particularly when the spreading rate surpasses the threshold of network resilience.

Numerical Results

For a quantitative insight, the improved method consistently showed a higher Kendall's tau value compared to other indices, especially in real-world settings where the spreading rate exceeded the epidemiological threshold. The results illustrate that nodes closer to the network core exhibit higher influence on spreading dynamics than their $k$-core values alone would suggest. Moreover, this method proves effective even in the Barabási-Albert model, which presented challenges for traditional $k$-shell decomposition due to uniform $k_s$ values among most nodes.

Implications and Future Directions

From a theoretical standpoint, this method contributes to the broader discourse on network centrality measures, enriching the landscape with a parameter-free approach that integrates spatial network properties. Practically, it facilitates more accurate identification of key influencers in network systems, which is invaluable for strategies aiming to control spreading processes. Given the observed performance improvements, future research could explore applying this methodology to larger and more diverse network types, further refining the theoretical models of influence spreading.

It remains to be seen how this method will evolve to incorporate dynamic changes in network topology or adapt to networks with non-standard structures. Moreover, integrating this method with other advanced centrality measures could provide even deeper insights into network dynamics and complexities.

Conclusion

This work enhances our capability to rank node influence with greater accuracy, offering a pragmatic solution to one of the long-standing challenges in network science. The introduction of the shortest path consideration to network core positions the methodology as a valuable tool for researchers and practitioners focusing on network resilience, information dissemination, and infection control strategies.