Identifying influential spreaders in complex networks based on gravity formula (1505.02476v3)

Abstract: How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks. We also use the classical Susceptible-Infected-Recovered (SIR) epidemic model to verify the good performance of our method.

Identifying Influential Spreaders in Complex Networks: A Gravity-Based Approach

The identification of pivotal nodes in complex networks is a task of significant importance across multiple domains, including information dissemination, disease control, and social influence. The paper "Identifying influential spreaders in complex networks based on gravity formula" by Ling-ling Ma et al. introduces an innovative method centered around the concept of gravity, overlooked by traditional measures such as degree centrality, betweenness centrality, and k-shell decomposition.

Methodology

The authors propose the gravity centrality index, a novel measure inspired by Newton's gravity formula. This method treats the k-shell value of a node as its "mass" and the shortest path distance between two nodes as their "distance." The concept diverges from traditional centrality measures by integrating a node's local topology and its connectivity to more distanced nodes. The gravity centrality index is operationalized as follows:

$$G(i) = \sum_{j \in \psi_i} \frac{ks(i) \cdot ks(j)}{d_{ij}^2}$$

where $ks(i)$ is the k-shell value of node $i$, and $d_{ij}$ is the shortest path distance between nodes $i$ and $j$. The set $\psi_i$ includes neighbors up to a predefined radius $r$. An extended variant, $G_+(i)$, further accounts for the gravity centrality of neighboring nodes.

Experimental Validation

The effectiveness of the gravity centrality index was validated using both real-world network datasets and synthetic models, specifically focusing on its correlation with spreading impact derived from the Susceptible-Infected-Recovered (SIR) model. Compared with existing centrality measures, gravity centrality demonstrated superior resolution and better performance in assessing node influence.

A new measure of monotonicity, $M(X)$, quantified the accuracy of ranking node influence, revealing higher precision in the gravity centrality index. Correlation analyses, using Kendall's tau coefficient, further confirmed that gravity centrality indices ($G$ and $G_+$) correlated more closely with nodes’ actual spreading power in networks than other metrics.

Implications and Future Directions

The results suggest that incorporating aspects of global network topology via the gravity formula yields a more nuanced and effective measure of node influence. This approach could potentially be extrapolated to weighted networks by redefining node mass or applied to multiplex and dynamic networks, which are pervasive in real-world contexts.

Looking forward, future research might explore adaptive algorithms to ascertain the optimal neighborhood radius $r$ automatically or integrate gravity centrality with other dynamic properties of networks to further enhance its robustness and applicability to diverse network configurations. This work offers a substantial contribution to the field of network science, providing a new lens through which to assess node centrality with implications that resonate across various application domains.