Structure of triadic relations in multiplex networks

Cozzo, Emanuele; Kivelä, Mikko; Domenico, Manlio De; Solé-Ribalta, Albert; Arenas, Àlex; Gómez, Sergio; Porter, Mason A.; Moreno, Yamir

doi:10.1088/1367-2630/17/7/073029

Cited by 93 publications

(80 citation statements)

References 58 publications

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“…For example, a biological system can be studied at the protein, RNA or gene level [29], and similarly, social networks can be studied by taking into account a person's presence on multiple platforms [21]. For computational purposes, such networks are commonly represented in the form of supra-adjacency matrices, where block-diagonal structure, connecting the same node across individual layers emerges [9]. Algorithms can operate on such matrices directly and thus exploit such additional information representing multiple aspects.…”

Section: Multiplex Networkmentioning

confidence: 99%

Patterns of Multiplex Layer Entanglement Across Real and Synthetic Networks

Škrlj

Renoust

2019

Complex Networks and Their Applications VIII

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Real world complex networks often exhibit multiplex structure, connecting entities from different aspects of physical systems such as social, transportation and biological networks. Little is known about general properties of such networks across disciplines. In this work, we first investigate how consistent are connectivity patterns across 35 real world multiplex networks. We demonstrate that entanglement homogeneity and intensity, two measures of layer consistency, indicate apparent differences between social and biological networks. We also investigate trade, co-authorship and transport networks. We show that real networks can be separated in the joint space of homogeneity and intensity, demonstrating the usefulness of the two measures for categorization of real multiplex networks. Finally, we design a multiplex network generator, where similar patterns (as observed in real networks), are emerging over the analysis of 11,905 synthetic multiplex networks with various topological properties.

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Section: Multiplex Networkmentioning

confidence: 99%

Patterns of Multiplex Layer Entanglement Across Real and Synthetic Networks

Škrlj

Renoust

2019

Complex Networks and Their Applications VIII

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“…The statistics of cycles is relevant both from a theoretical and an applicative point of view. From a theoretical perspective, it allows one to understand whether the distribution of cycles observed in a real world network is significantly different from that in a random graph with similar statistics [10]. Even in the single layer case, the high concentration of finite cycles in real-world networks has been a formidable barrier to analytic treatment, as mathematical models of large networks are typically based on the local tree-like assumption, i.e.…”

mentioning

confidence: 99%

Cycles and clustering in multiplex networks

et al. 2016

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In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of switches between layers. We calculate the expected number of cycles of each type in the configuration model of a large sparse multiplex network. Our method accounts for the full degree distribution including correlations between degrees in different layers. In particular, we obtain the numbers of cycles of length 3 of all possible types. Using these, we give a complete set of clustering coefficients and their expected values. We show that correlations between the degrees of a vertex in different layers strongly affect the number of cycles of a given type, and the number of switches between layers. Both increase with assortative correlations and are strongly decreased by disassortative correlations. The effect of correlations on clustering coefficients is equally pronounced.

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“…Many methods and measures developed for single layer networks have been extended to be applicable to multilayer networks [5], [43], [44], [45], [46]. In this context new community detection methods have been devised, mainly by reusing concepts already developed for single layer networks.…”

Section: Workmentioning

confidence: 99%

Multilayer Flows in Molecular Networks Identify Biological Modules in the Human Proteome

Mangioni

Jurman

Domenico

2020

IEEE Trans. Netw. Sci. Eng.

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A variety of complex systems exhibit different types of relationships simultaneously that can be modeled by multiplex networks. A typical problem is to determine the community structure of such systems that, in general, depend on one or more parameters to be tuned. In this study we propose one measure, grounded on information theory, to find the optimal value of the relax rate characterizing Multiplex Infomap, the generalization of the Infomap algorithm to the realm of multilayer networks. We evaluate our methodology on synthetic networks, to show that the most representative community structure can be reliably identified when the most appropriate relax rate is used. Capitalizing on these results, we use this measure to identify the most reliable meso-scale functional organization in the human protein-protein interaction multiplex network and compare the observed clusters against a collection of independently annotated gene sets from the Molecular Signatures Database (MSigDB). Our analysis reveals that modules obtained with the optimal value of the relax rate are biologically significant and, remarkably, with higher functional content than the ones obtained from the aggregate representation of the human proteome. Our framework allows us to characterize the meso-scale structure of those multilayer systems whose layers are not explicitly interconnected each other -as in the case of edge-colored models -the ones describing most biological networks, from proteomes to connectomes. ! arXiv:1801.10144v1 [q-bio.MN] 30 Jan 2018 • GN/ER. This system is generated by combining an Erdos-Renyi layer with one generated by the Girvan-Newman (GN) benchmark [9]. A community structure is only present in the GN layer, hence this multiplex network is used to test the impact of coupling noise to a structured population.• GN/GN. This system consists of two GN networks, with tunable cross-layer community overlap, generated as following. First, we create a single-layered GN network and duplicate it to generate a multiplex network with two layers. Then, in second layer, we iteratively swap the neighbours of pairs of randomly selected nodes to change the community structure. The swapping procedure is repeated until the ratio of community overlapping across layers, defined by the fraction of nodes that belong to the same communities across layers, is reached. Two classes of networks are generated, corresponding to a different amount of overlapping across layers (50% and 10%, respectively).• GN/CGN. This system consists of two layers, one GN network and one complementary GN (CGN). In order to explain how these two layers are generated,

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Structure of triadic relations in multiplex networks

Cited by 93 publications

References 58 publications

Patterns of Multiplex Layer Entanglement Across Real and Synthetic Networks

Patterns of Multiplex Layer Entanglement Across Real and Synthetic Networks

Cycles and clustering in multiplex networks

Multilayer Flows in Molecular Networks Identify Biological Modules in the Human Proteome

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