Structural reducibility of multilayer networks

Abstract

Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.

Multilayer network modeling of integrated biological systems

“…To this aim, multiples sources of omics data encode different layers, representing a biological system as a network of networks. This integrated perspective allows for more predictive performances [17,18,19] and has been shown to better characterize the evolution of complex diseases such as cancer [20], as well as to better understand the response to genetic and metabolic perturbations in complex organisms like E. coli [21].…”

Characterizing interactions in online social networks during exceptional events

“…As just discussed, each kind of activity on Twitter (retweet, reply, and mention) represents a particular kind of interaction between two users. Therefore, an appropriate framework to capture the overall structure of these interactions without loss of information about the different types is the framework of multilayer networks [22][23][24][25][26][27]. More specifically, in the case under investigation the more appropriate model is given by edge-colored graphs, particular multilayer networks The second column reports the total number of nodes and edges, corresponding to a network in which information is aggregated.…”

“…This information can be obtained by calculating the edge overlap [26,30] between each pair of layers. However, when the number of edges is very heterogeneous across layers, a more suitable descriptor of edge overlap is given by:…”

A multilayer protein-protein interaction network analysis of different life stages in Caenorhabditis elegans

“…Formally, L G has all the properties of a density matrix i.e., it is positive semi-definite and T r(L G ) = 1 [21]. Therefore, S α can be written as,…”