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.
Highlights
Despite recent advances [1,2,3,4] in the analysis of complex networks, a number of areas of investigation concerned with the description, prediction, and control of the dynamics of a variety of systems, including weather networks [5], social networks [6], and the brain [7], still remain largely unexplored
Our results show that the Multiplicative Multiplex PageRank of users displays a broad distribution, and is able to capture the emergence of high-ranked nodes, unlike what can be obtained through the application of the PageRank centrality measure to a single network
We apply the Multiplex PageRank measure to the multiplex network created from an online community at the University of California, Irvine [52]
Summary
Despite recent advances [1,2,3,4] in the analysis of complex networks, a number of areas of investigation concerned with the description, prediction, and control of the dynamics of a variety of systems, including weather networks [5], social networks [6], and the brain [7], still remain largely unexplored. A large number of these systems cannot be properly understood unless they are regarded as components of higher-level systems in which various networks are connected with one another through a complex pattern of interdependencies [6,8,9,10] These higher-level systems can be seen as networks in which the interacting nodes are networks themselves that are characterized by their own structure and function, and co-evolve over time according to various patterns. To uncover the nature and full breadth of social interaction, a special emphasis should be placed precisely on the structure and dynamics of the network of interacting social networks
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