Consensus ranking for multi-objective interventions in multiplex networks

Multiplex networks are representations of multilayer interconnected complex networks where the nodes are the same at every layer. They turn out to be good abstractions of the intricate connectivity of multimodal transportation networks, among other types of complex systems. One of the most important critical phenomena arising in such networks is the emergence of congestion in transportation flows. Here, we prove analytically that the structure of multiplex networks can induce congestion for flows that otherwise would be decongested if the individual layers were not interconnected. We provide explicit equations for the onset of congestion and approximations that allow us to compute this onset from individual descriptors of the individual layers. The observed cooperative phenomenon is reminiscent of Braess' paradox in which adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. Similarly, in the multiplex structure, the efficiency in transportation can unbalance the transportation loads resulting in unexpected congestion.

Complex networks recently opened new ways for investigating how language use is influenced by the mental representation of word similarities. This work adopts the framework of multiplex lexical networks for investigating lexical retrieval from memory. The focus is on priming, i.e., exposure to a given stimulus facilitating or inhibiting retrieval of a given lexical item. Supported by recent findings of network distance influencing lexical retrieval, the multiplex network approach tests how the layout of hundreds of thousands of word‐word similarities in the mental lexicon can lead to priming effects on multiple combined semantic and phonological levels. Results provide quantitative evidence that phonological priming effects are encoded directly in the multiplex structure of the mental representation of words sharing phonemes either in their onsets (cohort priming) or at their ends (rhyme priming). By comparison with randomised null models, both cohort and rhyming effects are found to be emerging properties of the mental lexicon arising from its multiplexity. These priming effects are absent on individual layers but become prominent on the combined multiplex structure. The emergence of priming effects is displayed both when only semantic layers are considered, an approximated representation of the so‐called semantic memory, and when semantics is enriched with phonological similarities, an approximated representation of the lexical‐auditory nature of the mental lexicon. Multiplex lexical networks can account for connections between semantic and phonological information in the mental lexicon and hence represent a promising modelling route for shedding light on the interplay between multiple aspects of language and human cognition in synergy with experimental psycholinguistic data.

The problem of aggregating individual rankings to create an overall consensus ranking representative of the group is of longstanding interest in group decision making. The problem arises in situations where a group of k Decision Makers (DMs) are asked to rank order n alternatives. The question is how to combine the DMs' rankings into one consensus ranking. Several different approaches have been suggested to aggregate DM responses into a compromise or consensus ranking, however, none is generally recognised as being the best and the similarity of consensus rankings generated by these algorithms is largely unknown. In this paper, we propose a new Weighted-sum ordinal Consensus ranking Method (WCM) with the weights derived from a Sigmoid function. We run Monte Carlo simulation across a range of k and n to compare the similarity of the consensus rankings generated by our method with the best-known method of Borda-Kendall (BAK; Kendall, M. (1962) Rank correlation methods. New York, NY: Hafner) and two other commonly used techniques proposed by Beck, M.P. and Lin, B.W. (1983) 'Some heuristics for the consensus ranking problem', Computers and Operations Research, Vol. 10,

The analysis of the advisor-advisor relationship can provide rich information for understanding the interactions among entities in academic network. Most of the existing methods mine the relationship in collaboration network. They focus on extracting deep relationships between attributes, but ignore the structure of nodes. Compared with the multiplex network, the collaboration network can only provide a single view, which describes whether the two nodes have co-authored publications. To tackle these problems, we propose an Attention-based Multiplex Network Structure Fusion (AMNSF) method for mining the advisor-advisee relationship. AMNSF takes the multiplex network as input composed of the acknowledgment network and the collaboration network where the acknowledgment network provides the social relationship between entities. We make full use of the network’s structure information and design a novel network fusion mechanism to integrate the structure information from each layer. Finally, we conduct extensive experiments on a variety of datasets. The experimental results show that the proposed model outperforms the state-of-the-art methods.KeywordsAdvisor-advisee relationshipGraph neural networkMultiplex networkScientific collaboration network

Multiplex network community detection algorithm based on motif awareness

Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in the multiplex networks structure, such as the overlap of the links in different layers. Many multiplex networks are also weighted, and the weights of the links can be strongly correlated with the structural properties of the multiplex network. For example, in multiplex network formed by the citation and collaboration networks between PRE scientists it was found that the statistical properties of citations to coauthors differ from the one of citations to noncoauthors, i.e., the weights depend on the overlap of the links. Here we present a theoretical framework for modeling multiplex weighted networks with different types of correlations between weights and overlap. To this end, we use the framework of canonical network ensembles, and the recently introduced concept of multilinks, showing that null models of a large variety of network structures can be constructed in this way. In order to provide a concrete example of how this framework apply to real data we consider a multiplex constructed from gene expression data of healthy and cancer tissues.

We develop graphlet analysis for multiplex networks and discuss how this analysis can be extended to multilayer and multilevel networks as well as to graphs with node and/or link categorical attributes. The analysis has been adapted for two typical examples of multiplexes: economic trade data represented as a 957-plex network and 75 social networks each represented as a 12-plex network. We show that wedges (open triads) occur more often in economic trade networks than in social networks, indicating the tendency of a country to produce/trade of a product in local structure of triads which are not closed. Moreover, our analysis provides evidence that the countries with small diversity tend to form correlated triangles. Wedges also appear in the social networks, however the dominant graphlets in social networks are triangles (closed triads). If a multiplex structure indicates a strong tie, the graphlet analysis provides another evidence for the concepts of strong/weak ties and structural holes. In contrast to Granovetter’s seminal work on the strength of weak ties, in which it has been documented that the wedges with only strong ties are absent, here we show that for the analyzed 75 social networks, the wedges with only strong ties are not only present but also significantly correlated.

Who influences whom and how in river-basin governance?A participatory stakeholder and social network analysis in Zayandeh-Rud basin, Iran

Online users are typically active on multiple social media networks (SMNs), which constitute a multiplex social network. With improvements in cybersecurity awareness, users increasingly choose different usernames and provide different profiles on different SMNs. Thus, 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 (MulCEVs). 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. In addition, MulCEV models the layers as weighted graphs to obtain 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 and synthetic datasets demonstrate that the proposed MulCEV framework markedly outperforms current embedding-based methods, especially when the number of training iterations is small.

This paper elaborates on two theories of social influence processes to multiplex network structures. First, cohesion influence is based on mutual communication made by different types of relations, and second comparison influence that is built on contrasting types of tie. While a system of bundles with a mutual character constitutes the setting for a multiplex network exposure measure within cohesion, comparison influence is defined algebraically through classes of actors in terms of a weakly balanced semiring structure that considers positive, negative, and also ambivalent types of tie. A case study with these approaches is made on an entrepreneurial community network with formal business relations, informal friendship ties, and perceived competition among the firms, and the methods are validated with the Sampson Monastery data set.

Multiplex networks (MNs) have become a platform of recent research in network sciences because networks in many real-world systems interact and function together. One of the main scientific issues in MNs is how the interdependence changes the emerging patterns or phase transitions. Until now, studies of such an issue have concentrated on cluster-breakdown phenomena, aiming to understand the resilience of the system under random failures of edges. These studies have revealed that various phase transition (PT) types emerge in MNs. However, such studies are rather limited to percolation-related problems, i.e., the limit q→1 of the q-state Potts model. Thus, a systematic study of opinion formation in social networks with the effect of interdependence between different social communities, which may be seen as the study of the emerging pattern of the Ising model on MNs, is needed. Here we study a well-known spin model called the Ashkin-Teller (AT) model in scale-free networks. The AT model can be regarded as a model for interacting systems between two species of Ising spins placed on respective layers in double-layer networks. Our study shows that, depending on the interlayer coupling strength and a network topology, unconventional PT patterns can also emerge in interaction-based phenomena: continuous, discontinuous, successive, and mixed-order PTs and a continuous PT not satisfying the scaling relation. The origins of such rich PT patterns are elucidated in the framework of Landau-Ginzburg theory.

Multiplex networks have been widely used to describe the multi-type connections of entities in the real world. However, researches for multiplex networks visualization unilaterally focus on the presentation of topological structure, lacking of specific high-level information presentation for quantitative comparison of interlayer structure. Users cannot participate in the exploration and freely choose the layers (or sub-graphs, regions, etc.) of interest for structural comparison. Contraposing the layer-edge patterns visual analysis tasks of multiplex networks, this paper puts forward a novel solution for exploration and analysis that tightly couples topological structure and high-level patterns. It mainly contains a multi-force directed model to realize the balanced layout of nodes in multi-layer topology, as well as two kinds of high-level patterns of which the visual representations are, respectively, designed by a familiar metaphor—that is, the similar pattern representation based on the area-proportional Venn diagrams and the interaction pattern representation based on the directed arrows. Furthermore, views association is implemented through underlying data sharing and multiple interactions which can be used to gain insights through the creation of selections of interest and produce high-level infographic-style overviews simultaneously. The experiments on real-world data demonstrate the support of the proposed method for layer-edge patterns analysis tasks in multiplex networks and the effectiveness for analyzing the multi-layer structure of multiplex networks.

Community detection in social networks is a promising research area. However, network exploration with multiple types of relationships remains an underexplored yet crucial domain. To address the challenge of community detection in multiplex networks, we propose SFCSA, a smart flattening-based Cuckoo Search Algorithm, designed to address the complexities of such networks effectively. SFCSA unfolds in three integral steps. Firstly, we employ DeepWalk and node2vec algorithms to extract node embeddings, which are merged to construct the multiplex network node embeddings, minimizing information loss. Secondly, a flattened network is built by merging the network layers and adopting the Pearson correlation coefficient as a weight to capture node similarity. Thirdly, we employ a community detection approach that unveils the community structure through a cuckoo search algorithm applied to the multiplex node embeddings to extract the best set of cluster centres by maximizing the modularity function. Experimental evaluations across synthetic and real-world multiplex networks attest to the efficiency and effectiveness of our approach, outperforming state-of-the-art algorithms.

Modern society is increasingly massively connected, reflecting an omnipresent tendency to organize social, economic, and technological structures in complex networks. Recently, with the advent of the so-called multiplex networks, new concepts and tools were necessary to better understand the characteristics of this type of system, as well as to analyze and quantify its performance and efficiency. The concept of diversity in multiplex networks is a striking example of this intrinsically interdisciplinary effort to better understand the nature of complex networks. In this work, we introduce the Multiplex Efficiency Index, which allows quantifying the temporal evolution of connectivity diversity, particularly when the number of layers of the multiplex network varies over time. Using data related to air passenger transportation in Brazil we investigate, through the new index, how the Brazilian air transportation network has being changing over the years due to the privatization processes of airports and mergers of airlines in Brazil. Besides that, we show how the Multiplex Efficiency Index is able to quantify fluctuations in network efficiency in a non-biased way, limiting its values between 0 and 1, taking into account the number of layers in the multiplex structure. We believe that the proposed index is of great value for the evaluation of the performance of any multiplex network, and to analyze, in a quantitative way, its temporal evolution independently of the variation in the number of layers.

Synchronization phenomenon plays an important role in the dynamic process on complex networks. In this letter, we consider synchronization under multiplex structures and explore the effect of external parts on the multilayered Kuramoto model with positive correlation between frequencies and degree. We show that large and strong mixing parts of the external layer may put off synchronization while the coupling strength of external layers has an accelerating, but limited, influence on synchronization. In particular, an explosive synchronization can be obtained by weakening the co-evolution coupling strength. The transition tends to be smooth when the co-evolution coupling strength increases. Our findings indicate that externality from multiplex networks, especially the mixing parts, and the co-evolution coupling strength should be of importance for synchronization on one certain layer.