On degree-degree correlations in multilayer networks

We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to weighted networks and provides information about correlations considering pairs of layers. By analyzing the multilayer representation of the airport transportation network, we show that contrasting results are obtained when the layers are analyzed independently or as an interconnected system. Finally, we study the impact of the level of assortativity and heterogeneity between layers on the spreading of diseases. Our results highlight the need of studying degree-degree correlations on multilayer systems, instead of on aggregated networks.Comment: 8 pages, 3 figure

A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks

Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.Comment: 57 pages, 10 figure

Disease Localization in Multilayer Networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.Comment: Revised version. 25 pages and 18 figure

Opportunities and challenges in partitioning the graph measure space of real-world networks

Based on a large dataset containing thousands of real-world networks ranging from genetic, protein interaction, and metabolic networks to brain, language, ecology, and social networks we search for defining structural measures of the different complex network domains (CND). We calculate 208 measures for all networks and using a comprehensive and scrupulous workflow of statistical and machine learning methods we investigated the limitations and possibilities of identifying the key graph measures of CNDs. Our approach managed to identify well distinguishable groups of network domains and confer their relevant features. These features turn out to be CND specific and not unique even at the level of individual CNDs. The presented methodology may be applied to other similar scenarios involving highly unbalanced and skewed datasets

Disease localization in multilayer networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptibleinfected- recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes

Discordant attributes of structural and functional brain connectivity in a two-layer multiplex network.

Several studies have suggested that functional connectivity (FC) is constrained by the underlying structural connectivity (SC) and mutually correlated. However, not many studies have focused on differences in the network organization of SC and FC, and on how these differences may inform us about their mutual interaction. To explore this issue, we adopt a multi-layer framework, with SC and FC, constructed using Magnetic Resonance Imaging (MRI) data from the Human Connectome Project, forming a two-layer multiplex network. In particular, we examine node strength assortativity within and between the SC and FC layer. We find that, in general, SC is organized assortatively, indicating brain regions are on average connected to other brain regions with similar node strengths. On the other hand, FC shows disassortative mixing. This discrepancy is apparent also among individual resting-state networks within SC and FC. In addition, these patterns show lateralization, with disassortative mixing within FC subnetworks mainly driven from the left hemisphere. We discuss our findings in the context of robustness to structural failure, and we suggest that discordant and lateralized patterns of associativity in SC and FC may provide clues to understand laterality of some neurological dysfunctions and recovery

Fundamentals of spreading processes in single and multilayer complex networks

Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In the last two decades, with the advent of modern network science, we have witnessed significant advances in this field of research. Here we review the main theoretical and numerical methods developed for the study of spreading processes on complex networked systems. Specifically, we formally define epidemic processes on single and multilayer networks and discuss in detail the main methods used to perform numerical simulations. Throughout the review, we classify spreading processes (disease and rumor models) into two classes according to the nature of time: (i) continuous-time and (ii) cellular automata approach, where the second one can be further divided into synchronous and asynchronous updating schemes. Our revision includes the heterogeneous mean-field, the quenched-mean field, and the pair quenched mean field approaches, as well as their respective simulation techniques, emphasizing similarities and differences among the different techniques. The content presented here offers a whole suite of methods to study epidemic-like processes in complex networks, both for researchers without previous experience in the subject and for experts.Comment: Review article. 73 pages, including 24 figure

Self-Organising Networks in Complex Infrastructure Projects: The Case of London Bank Station Capacity Upgrade Project

Managing large infrastructure projects remains a thorny issue in theory and practice. This is mainly due to their increasingly interconnected, interdependent, multilateral, nonlinear, unpredictable, uncontrollable, and rapidly changing nature. This study is an attempt to demystify the key issues to the management of large construction projects, arguing that these projects are delivered through networks that evolve in ways that we do not sufficiently understand as yet. The theoretical framework of this study is grounded in Complexity Theory; a theory resulted in a paradigm shift when it was first introduced to project management post-2000 but is yet to be unpacked in its full potential. The original contribution of the study is predicated on perceiving large construction projects as evolving complex systems that involves a high degree of self‐organisation. This is a process that transitions contractually static prescribed roles to dynamic network roles, comprising individuals exchanging information. Furthermore, by placing great emphasis upon informal communications, this study demonstrates how self-organising networks can be married with Complexity Theory. This approach has the potential to make bedfellows around the concept of managing networks within a context of managing projects; a concept that is not always recognised, especially in project management. With the help of social network analysis, two snapshots from Bank Station Capacity Upgrade Project Network were analysed as a case study. Findings suggest that relationships and hence network structures in large construction projects exhibit small-world topology, underlined by a high degree of sparseness and clustering. These are distinct structural properties of self-organising networks. Evidence challenges the theorisation about self-organisation which largely assumes positive outcomes and suggests that self-organising could open up opportunities yet also create constraints. This helps to provide further insights into complexity and the treatment of uncertainty in large projects. The study concludes with detailed recommendations for research and practice