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Multiplex networks convey more valuable information than single-layer networks; thus, performing the community detection task involving these networks has become a subject of extensive research on the exploration of latent community structures. The non-negative matrix factorization (NMF) algorithm has proven successful in community detection scenarios by offering good interpretations of community structures. However, directly obtaining consensus community assignments using the traditional NMF algorithm poses a challenge due to the presence of complex structures spanning across different layers in the multiplex network. In this paper, we propose a novel algorithm called Deep Structure-Preserving Non-negative Matrix Factorization (DSP-NMF) to perform community detection in multiplex networks. Specifically, DSP-NMF constructs a deep autoencoder-like NMF model to generate meaningful network embeddings that are represented by multiple basis matrices and reconstructed by corresponding transposed basis matrices. By integrating the similarity relationships of nodes into the proposed DSP-NMF algorithm, the corresponding Laplacian matrices in each network layer are regularized to preserve the community structure during the learning process. Simultaneously, a consensus network embedding can be learned to obtain the final community partition. In this manner, the proposed DSP-NMF algorithm not only uncovers robust community structures in multiplex networks but also maintains the coherence between layers without losing complementary features. The experimental results obtained on five multiplex network datasets show that our proposed DSP-NMF algorithm outperforms other competitive methods in community detection tasks involving multiplex networks. [ABSTRACT FROM AUTHOR]

In this paper, a meaningful representation of the road network using multiplex networks and a novel feature selection framework that enhances the predictability of future traffic conditions of an entire network are proposed. Using data on traffic volumes and tickets’ validation from the transportation network of Athens, we were able to develop prediction models that not only achieve very good performance but are also trained efficiently, do not introduce high complexity and, thus, are suitable for real-time operation. More specifically, the network’s nodes (loop detectors and subway/metro stations) are organized as a multilayer graph, each layer representing an hour of the day. Nodes with similar structural properties are then classified in communities and are exploited as features to predict the future demand values of nodes belonging to the same community. The results reveal the potential of the proposed method to provide reliable and accurate predictions.

Nowadays, community detection is one of the important fields for understanding network topology and has many applications in information diffusion, interaction mining and migration behaviour analysis. Therefore, community detection in social networks can help to understand user behaviour and network characteristics. There are many community detection methods, which are often designed for single-layer social networks. However, real-world networks use several types of relationships to establish connections between users, each of which has different characteristics. Hence, real-world networks can be modelled as multiplex networks. In general, multiplex networks are an example of multilayer networks in which the relationships between users in different networks can be considered simultaneously. In these networks, each layer represents the connections between users in a social network. Meanwhile, communities in multiplex networks are identified based on the structure and connections between overlapping users in different layers of the network. In this article, the nonnegative matrix tri-factorization (NMTF) strategy is used to model multiplex social networks, and a solution for community detection is developed based on it. According to this strategy, a common consensus matrix and then an alignment matrix are extracted based on similarity metrics and network structure. The use of these matrices as a flexible modelling framework enables the detection of coherent community between overlapping users in multiplex social networks. We evaluate the proposed NMTF method through various metrics on a multiplex social network. The results of this evaluation show the better performance of NMTF in terms of community quality compared to equivalent methods. [ABSTRACT FROM AUTHOR]

Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different ways necessitating the use of multiplex networks where multiple links are used to model the interactions. One of the major tools for inferring network topology is community detection. Although there are numerous works on community detection in single-layer networks, existing community detection methods for multiplex networks mostly learn a common community structure across layers and do not take the heterogeneity across layers into account. In this paper, we introduce a new multiplex community detection method that identifies communities that are common across layers as well as those that are unique to each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix Tri-Factorization, represents the adjacency matrix of each layer as the sum of two low-rank matrix factorizations corresponding to the common and private communities, respectively. Unlike most of the existing methods which require the number of communities to be pre-determined, the proposed method also introduces a two stage method to determine the number of common and private communities. The proposed algorithm is evaluated on synthetic and real multiplex networks, as well as for multiview clustering applications, and compared to state-of-the-art techniques.

Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In contrast, many existing models assume the same communities for all layers. Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples). This is appealing, since deciding the number of communities is a challenging aspect of community detection, and especially so in the multiplex setting, if one allows the communities to change across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a hierarchical Dirichlet prior to model community labels across layers, allowing dependency in their structure. Given the community labels, a stochastic block model (SBM) is assumed for each layer. We develop an efficient slice sampler for sampling the posterior distribution of the community labels as well as the link probabilities between communities. In doing so, we address some unique challenges posed by coupling the complex likelihood of SBM with the hierarchical nature of the prior on the labels. An extensive empirical validation is performed on simulated and real data, demonstrating the superior performance of the model over single-layer alternatives, as well as the ability to uncover interesting structures in real networks. [ABSTRACT FROM AUTHOR]

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.

Community detection is an effective exploration technique for analyzing networks. Most of the network data not only describes the connections of network nodes but also describes the properties of the nodes. In this paper, we propose a community detection method collects relevant evidences from the information of node attributes and the information of network structure to assist the community detection task on node-attributed networks. We find communities in the framework of the semidefinite programming (SDP) method. In practical applications, the distribution of some node attributes may be uncorrelated with the network structure or the network itself may contain no communities as in a random graph. A sparse attribute self-adjustment mechanism is introduced to determine the relative importance of each source of information. As a by product, our method is also effective for community detection of multilayer networks that allow for multiple kinds of relations over the same set of nodes. Experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we focus on the community detection problem in multiplex networks, that is, networks with multiple layers having the same node sets and no inter-layer connections. In particular, we look for groups of nodes that can be recognized as communities consistently across the layers. To this end, we propose a new approach that generalizes the Louvain method by (a) simultaneously updating the average and variance of the modularity scores across the layers and (b) reformulating the greedy search procedure in terms of a filter-based multiobjective optimization scheme. Unlike many previous modularity maximization strategies, which rely on some form of aggregation of the various layers, our multiobjective approach aims at maximizing the individual modularities on each layer simultaneously. We report experiments on synthetic and real-world networks, showing the effectiveness and the robustness of the proposed strategies both in the informative case, where all layers show the same community structure, and in the noisy case, where some layers represent only noise. [ABSTRACT FROM AUTHOR]

The integration of multi-source and diverse spatio-temporal travel data provides a comprehensive insight into urban mobility. Using data from Shenzhen's public transportation system, this study presents an analytical framework based on multiplex networks to examine variations in multi-mode public transportation usage (metro, bus, taxi, and shared bike) and their correlation with the built environment. This framework encompasses the analysis of network topological characteristics, centrality, and communities. The examination of network topological characteristics reveals that the multiplex transportation network exhibits high global accessibility and local connectivity. Network centrality analysis, focusing on weighted outdegree centrality, captures the patterns of public transportation ridership. Centrality modeling, employing the light gradient boosting machine, demonstrates a nonlinear relationship between ridership and the built environment. Factors including population density, residential land use percentage, entertainment service density, restaurant density, and metro station density consistently exhibit positive correlations with ridership across different times of the day. The community structure analysis, using consensus community detection, indicates that distinct urban areas exhibit clustering behavior based on public transportation demand patterns, forming distinct communities that closely align with the functional zoning of urban planning. These findings could provide valuable insights for the strategic planning of transportation services and the built environment. • Multi-source public transportation data are integrated to investigate urban mobility. • A multiplex network-based framework is developed to explore public transportation use. • Topological structure analysis reveals high global accessibility and local connectivity. • Centrality analysis reveals nonlinear correlations between ridership and the built environment. • Communities within multiplex networks closely align with the urban functional zoning. [ABSTRACT FROM AUTHOR]

A multiplex network models different modes of interaction among same-type entities. In this article, we provide a taxonomy of community detection algorithms in multiplex networks. We characterize the different algorithms based on various properties and we discuss the type of communities detected by each method. We then provide an extensive experimental evaluation of the reviewed methods to answer three main questions: to what extent the evaluated methods are able to detect ground-truth communities, to what extent different methods produce similar community structures, and to what extent the evaluated methods are scalable. One goal of this survey is to help scholars and practitioners to choose the right methods for the data and the task at hand, while also emphasizing when such choice is problematic. [ABSTRACT FROM AUTHOR]

Complex networks have been useful to link experimental data with mechanistic models, and have become widely used across many scientific disciplines. Recently, the increasing amount and complexity of data, particularly in biology, has prompted the development of multidimensional networks, where dimensions reflect the multiple qualitative properties of nodes, links or both. As a consequence, traditional quantities computed in single dimensional networks should be adapted to incorporate this new information. A particularly important problem is the detection of communities, namely sets of nodes sharing certain properties, which reduces the complexity of the networks, hence facilitating its interpretation.In this work, we propose an operative definition of 'function' for the nodes in multidimensional networks. We exploit this definition to show that it is possible to detect two types of communities: (a) modules, which are communities more densely connected within their members than with nodes belonging to other communities, and (b) guilds, which are sets of nodes connected with the same neighbours, even if they are not connected themselves. We provide two quantities to optimally detect both types of communities, whose relative values reflect their importance in the network.The flexibility of the method allowed us to analyse different ecological examples encompassing mutualistic, trophic and microbial networks. We showed that by considering both metrics we were able to obtain deeper ecological insights about how these different ecological communities were structured. The method mapped pools of species with properties that were known in advance, such as plants and pollinators. Other types of communities found, when contrasted with external data, turned out to be ecologically meaningful, allowing us to identify species with important functional roles or the influence of environmental variables. Furthermore, we found that the method was sensitive to community‐level topological properties like nestedness.In ecology there is often a need to identify groupings including trophic levels, guilds, functional groups or ecotypes. The method is therefore important in providing an objective means of distinguishing modules and guilds. The method we developed, functionInk (functional linkage), is computationally efficient at handling large multidimensional networks since it does not require optimization procedures or tests of robustness. The method is available at: https://github.com/apascualgarcia/functionInk. [ABSTRACT FROM AUTHOR]

Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NF-CCE), a new class of algorithms, based on four different non-negative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a non-negative, low-dimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common non-negative, low-dimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the state-of-the-art methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks. [ABSTRACT FROM AUTHOR]

Multiplex networks are a type of multilayer network in which entities are connected to each other via multiple types of connections. We propose a method, based on computing pairwise similarities between layers and then doing community detection, for grouping structurally similar layers in multiplex networks. We illustrate our approach using both synthetic and empirical networks, and we are able to find meaningful groups of layers in both cases. For example, we find that airlines that are based in similar geographic locations tend to be grouped together in a multiplex airline network and that related research areas in physics tend to be grouped together in a multiplex collaboration network. [ABSTRACT FROM AUTHOR]

Multilayer networks are a useful way to capture and model multiple, binary or weighted relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the development of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set through comparison with a fixed degree random graph model. Multilayer Extraction directly handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure can capture overlapping communities, as well as background vertex-layer pairs that do not belong to any community. We establish consistency of the vertex-layer set optimizer of our proposed multilayer score under the multilayer stochastic block model. We investigate the performance of Multilayer Extraction on three applications and a test bed of simulations. Our theoretical and numerical evaluations suggest that Multilayer Extraction is an effective exploratory tool for analyzing complex multilayer networks. Publicly available code is available at https://github.com/jdwilson4/MultilayerExtraction. [ABSTRACT FROM AUTHOR]

Detecting hidden communities is important for the analysis of complex networks. However, many algorithms have been designed for single layer networks (SLNs) while just a few approaches have been designed for multiplex networks (MNs). In this paper, we propose an algorithm based on layer reduction for detecting communities on MNs, which is termed as LRCD-MNs. First, we improve a layer reduction algorithm termed as neighaggre to combine similar layers and keep others separated. Then, we use neighaggre to find the community structure hidden in MNs. Experiments on real-life networks show that neighaggre can obtain higher relative entropy than the other algorithm. Moreover, we apply LRCD-MNs on some real-life and synthetic multiplex networks and the results demonstrate that, although LRCD-MNs does not have the advantage in terms of modularity , it can obtain higher values of surprise , which is used to evaluate the quality of partitions of a network. [ABSTRACT FROM AUTHOR]

Multiplex networks have shown high utility in modeling complex systems, e.g., academic social networks. Composite community structures contribute to revealing meaningful grouping patterns in multiplex networks. Multiplex network community detection, especially using higher-order interaction information, has become a popular research topic in complex network analysis. We propose a multiplex network community detection algorithm based on motif awareness (CDMA) to reduce information loss during the aggregation of multiplex networks, which can solve the community detection problem for cold start nodes and improve the quality of multiplex network community detection. Interlayer differences are fully considered in the topology of the multiplex network throughout the algorithm. First, the motif is used to mine the higher-order interaction information in each layer of the network topology, and a multiplex network aggregation model is constructed to aggregate the multiplex network into a single-layer composite network. In addition, the information propagation method is used to transform the node information in the single-layer composite network into a vector. Furthermore, we propose a node importance evaluation index and select the nodes with the greatest significance to solve the initial node selection sensitivity problem of the k -means algorithm. The comparative experimental results on real multiplex network datasets, e.g., SCHOLAT, show that the proposed CDMA algorithm can play an important role in addressing the issue of effective detection of the community structure of multiplex networks with higher accuracy. [ABSTRACT FROM AUTHOR]

Multiplex network is an emergent model that has been lately proposed in order to cope with the complexity of real-world networks. A multiplex network is defined as a multi-layer interconnected graph. Each layer contains the same set of nodes but interconnected by different types of links. This rich representation model requires to redefine most of the existing network analysis algorithms. In this paper we focus on the central problem of community detection. Most of existing approaches consist on transforming the problem, in a way or another, to the classical setting of community detection in a monoplex network. In this work, we propose a new approach that consists on adapting a seed-centric algorithm to the multiplex case. The first experiments on heterogeneous bibliographical networks show the relevance of the approach compared to the existing algorithms. [ABSTRACT FROM AUTHOR]

• We present a community-based link prediction in multiplex networks called CLPES. • CLPES employs the MOEA/D-TS method for community detection in multiplex networks. • We expand definitions of link types in multiplex networks. • We propose an external similarity measure between layers of multiplex networks. • Experiments on real networks show the superiority of the proposed CLPES. Multiplex link prediction is the problem of finding missing links between nodes based on information from other layers. Although the link prediction problem in the online social networks is studied comprehensively, most approaches only employ internal features of the under prediction layer and do not consider additional link information from other networks. Also, many existing link prediction techniques are only based on the extracted information from links or nodes. However, the information flow in many real-world systems like social networks is considered as collaborative relations on correlated groups as an alternative for individual relations. In this research, we have proposed a Community-guided Link Prediction based on External Similarity (CLPES) method for multiplex networks in which, beside nodes and links information, community information is also employed. In our proposed method, we used an evolutionary algorithm (MOEA/D-TS) for specifying the community structure of the desired network. Next, the incorporation of internal features of each layer with a new external similarity metric (ExSim) obtains the final values for the likelihood of link formation in the network. Experiments on various real-world multiplex networks prove the capability of the proposed CLPES method for producing improved results and its superiority against other link prediction algorithms. [Display omitted] [ABSTRACT FROM AUTHOR]

• The MOEA/D-TS is applied to detect shared communities in multiplex networks. • Improved MOEA/D-TS uses the clustering coefficient for the generation of initial population. • No prior knowledge on the number and size of communities is required. • Experiments on real networks show the superiority of the improved MOEA/D-TS. Multiplex networks are the general representative of complex systems composed of distinct interactions between the same entities on multiple layers. Community detection in the multiplex networks is the problem of finding a shared structure under all layers, which combines the information of the entire network. Most of the existing methods for community detection in the single-layer networks cannot be well applied to detect shared communities in multiplex networks. In this paper, we employ a multi-objective evolutionary approach, namely Multi-Objective Evolutionary Algorithm based on Decomposition with Tabu Search (MOEA/D-TS), to detect shared communities in multiplex networks. Also, we have improved the MOEA/D-TS using a social networks analysis measure named Clustering Coefficient (CC) in terms of the generation of the initial population. This hybrid algorithm employs the parallel computing capacity of the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) along with the neighborhood search authority of Tabu Search (TS) for discovering Pareto optimal solutions. Extensive experiments on a variety of single-layer and multiplex real-world data sets show the superiority of the proposed method in comparison to state-of-the-art algorithms and its capability for producing improved results. [ABSTRACT FROM AUTHOR]