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Register a new userThe weak core and the structure of elites in social multiplex networks
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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.
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Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant inter-layer correlations -- degree-degree correlation, edge overlap, node similarities -- able to make them robust against random and targeted failures of their individual components. Here, we show that inter-layer correlations are important also in the characterization of their $mathbf{k}$-core structure, namely the organization in shells of nodes with increasingly high degree. Understanding $k$-core structures is important in the study of spreading processes taking place on networks, as for example in the identification of influential spreaders and the emergence of localization phenomena. We find that, if the degree distribution of the network is heterogeneous, then a strong $mathbf{k}$-core structure is well predicted by significantly positive degree-degree correlations. However, if the network degree distribution is homogeneous, then strong $mathbf{k}$-core structure is due to positive correlations at the level of node similarities. We reach our conclusions by analyzing different real-world multiplex networks, introducing novel techniques for controlling inter-layer correlations of networks without changing their structure, and taking advantage of synthetic network models with tunable levels of inter-layer correlations.
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.
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.
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.
Online users are typically active on multiple social media networks (SMNs), which constitute a multiplex social network. It is becoming increasingly challenging to determine whether given accounts on different SMNs belong to the same user; this can be expressed as an interlayer link prediction problem in a multiplex network. To address the challenge of predicting interlayer links , feature or structure information is leveraged. Existing methods that use network embedding techniques to address this problem focus on learning a mapping function to unify all nodes into a common latent representation space for prediction; positional relationships between unmatched nodes and their common matched neighbors (CMNs) are not utilized. Furthermore, the layers are often modeled as unweighted graphs, ignoring the strengths of the relationships between nodes. To address these limitations, we propose a framework based on multiple types of consistency between embedding vectors (MulCEV). In MulCEV, the traditional embedding-based method is applied to obtain the degree of consistency between the vectors representing the unmatched nodes, and a proposed distance consistency index based on the positions of nodes in each latent space provides additional clues for prediction. By associating these two types of consistency, the effective information in the latent spaces is fully utilized. Additionally, MulCEV models the layers as weighted graphs to obtain better representation. In this way, the higher the strength of the relationship between nodes, the more similar their embedding vectors in the latent representation space will be. The results of our experiments on several real-world datasets demonstrate that the proposed MulCEV framework markedly outperforms current embedding-based methods, especially when the number of training iterations is small.
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