Extracting information from multiplex networks

Abstract

Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social, financial, engineering and biological networks as well. Extending our ability to analyze complex networks to multiplex network structures increases greatly the level of information that is possible to extract from Big Data. For these reasons characterizing the centrality of nodes in multiplex networks and finding new ways to solve challenging inference problems defined on multiplex networks are fundamental questions of network science. In this paper we discuss the relevance of the Multiplex PageRank algorithm for measuring the centrality of nodes in multilayer networks and we characterize the utility of the recently introduced indicator function Θ S for describing their mesoscale organization and community structure. As working examples for studying these measures we consider three multiplex network datasets coming for social science.Multilayer networks are formed by nodes connected by links describing interactions with different connotations. When the same set of nodes can be connected by different types of links, the resulting multilayer network, is also called a multiplex network. Most social networks are multiplex, since the same set of people might be connected by different types of social ties or might communicate through different means of communication. As networks are ultimately a way to encode information about a complex set of interactions one of the most pressing and challenging problem in network science is to extract relevant information from them. Here we show evidence that the Multiplex PageRank algorithm and the recently introduced indicator function Θ S are able to extract from multiplex networks an information than cannot be inferred by analyzing the single layers taken in isolation or the aggregated network in which links of different type are not distinguished.The vast majority of complex interacting systems, from social networks to the brain and the biological networks of the cell, are multilayer networks 1-3 . Multilayer networks are formed by several networks (layers) describing interactions of different nature and connotation. Therefore multilayer networks encode significant more information than the network which include all the interactions of the multilayer network but does not distinguishes between the different nature of the links. As a consequence of this, one the most pressing challenge in multiplex network theory is devising algorithms and numerical methods to extract relevant information from these network structures. a) Electronic mail: j.iacovacci@qmul.ac.uk b) Electronic mail: g.bianconi@qmul.ac.uk Multilayer networks can be distinguished in two wide classes: multiplex networks and networks of networks 1,3 . Network of networks are multilayer networks formed by layers constituted by different nodes. Examples of network of networks are comple...

Multilayer Brain Networks

“…The centrality of a node in a network is a measure of its importance within the network, and measures of centrality have been leveraged to uncover interesting brain organization. Many measures of centrality, including PageRank [41] have been extended to the multilayer setting [42,43,44,45]. In [15], multilayer PageRank centrality [44] is used as an input to a classifier which is able to discriminate between healthy and schizophrenic individuals significantly better than the single layer counterparts.…”

Layer Communities in Multiplex Networks

“…The crucial difference between our approach and that of Iacovacci et al [7,24] is that we measure the connection similarity (an edge-centric property) between two layers instead of a similarity in their node properties. We also calculate layer similarity based on a measure of edge overlaps instead of using an explicitly informationtheoretic approach.…”

“…We now compare connection similarity with Jaccard, JS [9], and mesoscopic [7] similarites by applying them to cluster airlines in the airline data set that we discussed in Section III B.…”

“…Past studies of layer similarities in multilayer networks have focused primarily on nodecharacteristic similarities, such as interlayer degree correlations and node-community similarities [7,13,14,21]. These ideas have yielded insights into phenomena such as the presence and consequences (e.g., on percolation and spreading processes) of nontrivial multiplex correlations in networks [22,23].…”

Assessing diversity in multiplex networks

“…As another example, air transportation networks are constituted by airports (the nodes), which are connected by routes (the links) of different airlines (the layers) [16][17][18][19][20][21]. Due to their huge socio-economical impact, a lot of efforts are being focused on understanding the structure and functionality of multiplex networks, by developing appropriated analysis tools [22][23][24][25][26][27][28][29], and characterizing new phenomena emerging due to the layered structure [30][31][32][33][34][35][36][37][38].In the context of multiplex networks, diversity refers to the variety of connectivity configurations the elements that constitute the network (i.e., the nodes and the layers) have. Why is important to measure the diversity of a multiplex system?…”