Spreading dynamics in complex networks (1312.6335v1)

Abstract: Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from the epidemic control, innovation diffusion, viral marketing, social movement to idea propagation. In this paper, we first display some of the most important theoretical models that describe spreading processes, and then discuss the problem of locating both the individual and multiple influential spreaders respectively. Recent approaches in these two topics are presented. For the identification of privileged single spreaders, we summarize several widely used centralities, such as degree, betweenness centrality, PageRank, k-shell, etc. We investigate the empirical diffusion data in a large scale online social community -- LiveJournal. With this extensive dataset, we find that various measures can convey very distinct information of nodes. Of all the users in LiveJournal social network, only a small fraction of them involve in spreading. For the spreading processes in LiveJournal, while degree can locate nodes participating in information diffusion with higher probability, k-shell is more effective in finding nodes with large influence. Our results should provide useful information for designing efficient spreading strategies in reality.

Spreading Dynamics in Complex Networks

The paper of spreading dynamics within complex networks addresses the critical problem of identifying influential nodes or "spreaders," a topic with relevance across multiple domains, such as public health, marketing, and social movements. The paper authored by Sen Pei and Hernán A. Makse discusses theoretical models that describe spreading processes and presents methodologies for locating influential spreaders within a network.

Theoretical Models of Spreading

The paper systematically reviews prominent theoretical models employed to describe the diffusion processes in complex networks.

1. Independent Interaction Models: These models are grounded in epidemiological studies and assume that each interaction between an infected and a susceptible node results in transmission with a certain probability. The Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) models are classic examples that help to elucidate the dynamics of epidemic spread across a network. Key insights include the concept of an epidemic threshold, particularly in networks with heavy-tailed degree distributions, where the threshold may vanish, leading to widespread epidemics.
2. Threshold Models: These models are particularly relevant in sociology and economics, where the adoption of new behaviors or innovations is contingent on the fraction of an individual's network that has already adopted them. The Linear Threshold Model highlights the influence of network structure and critical thresholds that can precipitate large-scale cascades.

Identifying Influential Spreaders

The paper discusses various methodologies for determining which nodes within a complex network have the highest potential to influence or spread information:

• Centrality Measures:
  • Degree Centrality is straightforward but may not always be indicative of a node’s influence, especially if high-degree nodes are situated at the network's periphery.
  • Betweenness Centrality measures a node's role within the shortest paths of a network, while Closeness Centrality gauges how quickly a node can disseminate information throughout the network.
  • Eigenvector and PageRank Centralities consider the connectivity and influence of neighboring nodes, making them sensitive to the broader network topology.
  • k-shell Decomposition identifies a node's position in the network hierarchy, with deeply situated nodes exhibiting higher influence due to robust connectivity paths.
• Path Counting and Dynamic Influence Measures: These methods assess the influence of nodes by accounting for possible walk paths within the network, which can provide superior predictions of influence compared to traditional centrality measures.

Empirical Analysis

The empirical component of the paper investigates the effectiveness of these measures using data from the LiveJournal social network. Analysis shows that:

• Different centrality measures reflect varied aspects of node influence, with degree centrality identifying nodes with significant participation in diffusion, while k-shell decompositions seem to better predict overall influence.
• Despite the widespread integration in networks like LiveJournal, only a small subset of nodes actively participates in spreading processes, underscoring the importance of precise influence measurement.

Practical Implications and Future Directions

The research findings have several implications:

1. Optimal Strategy Design: Understanding which nodes are most influential aids in formulating strategies to maximize overlap in information dissemination and epidemic control.
2. Network Resilience and Layout: Insights into network structure and node influence can inform strategies for enhancing robustness against disruptions.

Furthermore, there's a need for continued research in diverse network settings, including consideration of local measures when full topological data is not accessible. This paper's framework could be adapted and tested across varying domains to verify its wider applicability and potentially uncover universal principles of influence in complex networks.