Functional Multiplex PageRank

Abstract

Complex systems PACS 89.75.Fb -Structures and organization in complex systems PACS 89.75.Hc -Networks and genealogical treesAbstract -Recently it has been recognized that many complex social, technological and biological networks have a multilayer nature and can be described by multiplex networks. Multiplex networks are formed by a set of nodes connected by links having different connotations forming the different layers of the multiplex. Characterizing the centrality of the nodes in a multiplex network is a challenging task since the centrality of the node naturally depends on the importance associated to links of a certain type. Here we propose to assign to each node of a multiplex network a centrality called Functional Multiplex PageRank that is a function of the weights given to every different pattern of connections (multilinks) existent in the multiplex network between any two nodes. Since multilinks distinguish all the possible ways in which the links in different layers can overlap, the Functional Multiplex PageRank can describe important non-linear effects when large relevance or small relevance is assigned to multilinks with overlap. Here we apply the Functional Page Rank to the multiplex airport networks, to the neuronal network of the nematode C. elegans, and to social collaboration and citation networks between scientists. This analysis reveals important differences existing between the most central nodes of these networks, and the correlations between their so called pattern to success.

Multiplex network analysis of the UK over‐the‐counter derivatives market

“…They calculate multiplex centrality measures based on the works by Iacovacci et al (2016) and Rahmede et al (2017) by assigning weights (or influences) to each layer via a maximum likelihood procedure that targets economic growth. 4 Because in our dataset we do not have a way to realistically interpret interlinks, in this work, we have chosen to use the FMEC and the FMP, which generalize the multiplex centrality proposed in Iacovacci et al (2016) and do not rely on the existence of interlinks. Korniyenko et al (2018) consider a multiplex network in which layers correspond to different kinds of investments between countries.…”

“…In this paper, we extend the PageRank centrality measure recently introduced by Iacovacci et al (2016) to develop a new a FMP for applying to weighted multiplex network. In this section, we introduce two centrality measures for single-layered networks-the eigenvector centrality and the PageRank centrality-and we reinterpret them from the perspective of the propagation of shocks in a financial network.…”

“…These extensions are the Functional Multiplex Eigenvector Centrality (FMEC) and the Functional Multiplex PageRank (FMP), which are based on the work of Iacovacci et al (2016). These extensions are the Functional Multiplex Eigenvector Centrality (FMEC) and the Functional Multiplex PageRank (FMP), which are based on the work of Iacovacci et al (2016).…”

“…Second, in order to quantitatively estimate the vulnerability of financial institutions we develop and compare two extensions of the eigenvector centrality and of the PageRank centrality. These extensions are the Functional Multiplex Eigenvector Centrality (FMEC) and the Functional Multiplex PageRank (FMP), which are based on the work of Iacovacci et al (2016).…”

“…7 In most cases, the solution of X= f (X) such that X i ≥ 0, ∀i is unique and therefore independent of the initial point X (0) . 11 We note that this definition of the FMP differs from the original definition proposed in Iacovacci et al (2016). 9 To do this, we assume that ν ¼ 1=N∑ j 1 − μ1 ∑ k Akj X PR j .…”