Multiplex PageRank

Abstract

Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social networks where people are involved in different types of relationships and interact through various forms of communication media. The ranking of nodes in multiplex networks is one of the most pressing and challenging tasks that research on complex networks is currently facing. When pairs of nodes can be connected through multiple links and in multiple layers, the ranking of nodes should necessarily reflect the importance of nodes in one layer as well as their importance in other interdependent layers. In this paper, we draw on the idea of biased random walks to define the Multiplex PageRank centrality measure in which the effects of the interplay between networks on the centrality of nodes are directly taken into account. In particular, depending on the intensity of the interaction between layers, we define the Additive, Multiplicative, Combined, and Neutral versions of Multiplex PageRank, and show how each version reflects the extent to which the importance of a node in one layer affects the importance the node can gain in another layer. We discuss these measures and apply them to an online multiplex social network. Findings indicate that taking the multiplex nature of the network into account helps uncover the emergence of rankings of nodes that differ from the rankings obtained from one single layer. Results provide support in favor of the salience of multiplex centrality measures, like Multiplex PageRank, for assessing the prominence of nodes embedded in multiple interacting networks, and for shedding a new light on structural properties that would otherwise remain undetected if each of the interacting networks were analyzed in isolation.

(16 pages, 6 figures)

References in corpus (7)

• Diffusion dynamics on multiplex networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• Emergence of network features from multiplexity
• Random Walks on Multiplex Networks
• The backbone of the climate network
• Eigenvector centrality of nodes in multiplex networks
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• Measuring and modelling correlations in multiplex networks
• Percolation in Multiplex Networks with Overlap
• Weighted Multiplex Networks
• Towards real-world complexity: an introduction to multiplex networks
• The new challenges of multiplex networks: measures and models
• Structure of Triadic Relations in Multiplex Networks
• Random walk centrality in interconnected multilayer networks
• Centralities of Nodes and Influences of Layers in Large Multiplex Networks
• Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles
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• Non-linear growth and condensation in multiplex networks
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• Extracting Information from Multiplex Networks
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• Multilayer Network Science: from Cells to Societies
• A Network Science perspective of Graph Convolutional Networks: A survey
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