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Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a multitasking behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields.
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Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.
It has recently become possible to record detailed social interactions in large social systems with high resolution. As we study these datasets, human social interactions display patterns that emerge at multiple time scales, from minutes to months. On a fundamental level, understanding of the network dynamics can be used to inform the process of measuring social networks. The details of measurement are of particular importance when considering dynamic processes where minute-to-minute details are important, because collection of physical proximity interactions with high temporal resolution is difficult and expensive. Here, we consider the dynamic network of proximity-interactions between approximately 500 individuals participating in the Copenhagen Networks Study. We show that in order to accurately model spreading processes in the network, the dynamic processes that occur on the order of minutes are essential and must be included in the analysis.
Internet communication channels, e.g., Facebook, Twitter, and email, are multiplex networks that facilitate interaction and information-sharing among individuals. During brief time periods users often use a single communication channel, but then communication channel alteration (CCA) occurs. This means that we must refine our understanding of the dynamics of social contagions. We propose a non-Markovian behavior spreading model in multiplex networks that takes into account the CCA mechanism, and we develop a generalized edge-based compartmental method to describe the spreading dynamics. Through extensive numerical simulations and theoretical analyses we find that the time delays induced by CCA slow the behavior spreading but do not affect the final adoption size. We also find that the CCA suppresses behavior spreading. On two coupled random regular networks, the adoption size exhibits hybrid growth, i.e., it grows first continuously and then discontinuously with the information transmission probability. CCA in ER-SF multiplex networks in which two subnetworks are ErdH{o}s-R{e}nyi (ER) and scale-free (SF) introduces a crossover from continuous to hybrid growth in adoption size versus information transmission probability. Our results extend our understanding of the role of CCA in spreading dynamics, and may elicit further research.
Recent approaches on elite identification highlighted the important role of {em intermediaries}, by means of a new definition of the core of a multiplex network, the {em generalised} $K$-core. This newly introduced core subgraph crucially incorporates those individuals who, in spite of not being very connected, maintain the cohesiveness and plasticity of the core. Interestingly, it has been shown that the performance on elite identification of the generalised $K$-core is sensibly better that the standard $K$-core. Here we go further: Over a multiplex social system, we isolate the community structure of the generalised $K$-core and we identify the weakly connected regions acting as bridges between core communities, ensuring the cohesiveness and connectivity of the core region. This gluing region is the {em Weak core} of the multiplex system. We test the suitability of our method on data from the society of 420.000 players of the Massive Multiplayer Online Game {em Pardus}. Results show that the generalised $K$-core displays a clearly identifiable community structure and that the weak core gluing the core communities shows very low connectivity and clustering. Nonetheless, despite its low connectivity, the weak core forms a unique, cohesive structure. In addition, we find that members populating the weak core have the best scores on social performance, when compared to the other elements of the generalised $K$-core. The weak core provides a new angle on understanding the social structure of elites, highlighting those subgroups of individuals whose role is to glue different communities in the core.
Online social network (OSN) applications provide different experiences; for example, posting a short text on Twitter and sharing photographs on Instagram. Multiple OSNs constitute a multiplex network. For privacy protection and usage purposes, accounts belonging to the same user in different OSNs may have different usernames, photographs, and introductions. Interlayer link prediction in multiplex network aims at identifying whether the accounts in different OSNs belong to the same person, which can aid in tasks including cybercriminal behavior modeling and customer interest analysis. Many real-world OSNs exhibit a scale-free degree distribution; thus, neighbors with different degrees may exert different influences on the node matching degrees across different OSNs. We developed an iterative degree penalty (IDP) algorithm for interlayer link prediction in the multiplex network. First, we proposed a degree penalty principle that assigns a greater weight to a common matched neighbor with fewer connections. Second, we applied node adjacency matrix multiplication for efficiently obtaining the matching degree of all unmatched node pairs. Thereafter, we used the approved maximum value method to obtain the interlayer link prediction results from the matching degree matrix. Finally, the prediction results were inserted into the priori interlayer node pair set and the above processes were performed iteratively until all unmatched nodes in one layer were matched or all matching degrees of the unmatched node pairs were equal to 0. Experiments demonstrated that our advanced IDP algorithm significantly outperforms current network structure-based methods when the multiplex network average degree and node overlapping rate are low.
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