Functional Multiplex PageRank: the centrality is a function (Vol. 48 No. 2)
Multiplex networks are formed by a set of nodes connected by different types of interactions. The centrality of a node in a multiplex network depends on the influence one attributes to different types of connections. For example consider a multiplex of two layers formed by Lufthansa and British Airways flights. If we attribute maximum influence to Lufthansa flights Frankfurt airport is more central than Heathrow airport while the opposite is true if we attribute maximum influence to British Airways flights. The Functional Multiplex PageRank combines this information through a paradigmatic shift: the centrality of a node is not a single number but an entire function associated to the relevance given to the different types of connections. For each node it allows to characterize which types of connections contribute the most to its centrality. Interestingly the correlations between the Functional Multiplex PageRank of different nodes reveal the similarity in the role of the nodes.
J. Iacovacci, C. Rahmede, A. Arenas and G. Bianconi,
, Functional Multiplex PageRank, EPL 116, 28004 (2016)