Real Multiplex Networks Research Articles

Hidden multiscale organization and robustness of real multiplex networks.

Hidden geometry enables the investigation of complex networks at different scales. Extending this framework to multiplex networks, we uncover a different kind of mesoscopic organization in real multiplex systems, named clan, a group of nodes that preserve local geometric arrangements across layers. Furthermore, we reveal the intimate relationship between the unfolding of clan structure and mutual percolation against targeted attacks, leading to an ambivalent role of clans: making a system fragile yet less prone to complete shattering. Finally, we confirm the correlation between the multiscale nature of geometric organization and the overall robustness. Our findings expand the significance of hidden geometry in network function, while also highlighting potential pitfalls in evaluating and controlling catastrophic failure of multiplex systems.

Robustness measurement of multiplex networks based on multiplex motifs

Multiplex network is a classic multilayer network model that can be used to model complex systems in the real world. Previous measures of network robustness mainly focused on the low-order characteristics of network topology, and the existence of motifs in the network is ignored. As simple building blocks of multiplex networks, multiplex motifs are indispensable tools to understand the structure of local networks. Therefore, from a mesoscopic perspective, we propose an index called normalized motif entropy to measure the robustness of multiplex networks under malicious attacks, and the effectiveness of our method is verified in real multiplex networks.

LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks

The individuals of real-world networks participate in various types of connections, each forming a layer in multiplex networks. Link prediction is an important problem in multiplex network analysis owing to its wide range of practical applications, such as mining drug targets, recommending friends in social networks, and exploring network evolution mechanisms. A key issue of link prediction within multiplex networks is how to estimate the likelihood of potential links in the predicted layer by leveraging both interlayer and intralayer information. Several studies have shown that incorporating interlayer topological information can improve the performance of link prediction in the predicted layer. Therefore, this paper proposes the Link Prediction based on Global Relevance of Interlayer (LPGRI) method to estimate the likelihood of potential links in the predicted layer of multiplex networks, which comprehensively utilizes both types of information. In the LPGRI method, the contribution of interlayer information is determined using the global relevance (GR) index between layers. Experimental studies on six real multiplex networks demonstrate the competitive performance of our method.

Vital node identification based on cycle structure in a multiplex network.

Multiplex networks frame the heterogeneous nature of real systems, where the multiple roles of nodes, both functionally and structurally, are well represented. We identify these vital nodes in a multiplex network so that we can control a pandemic outbreak like COVID-19, eliminate damage from a network attack, maintain traffic, and so on. Vital node identification has attracted scientists in various fields for decades. In this paper, we propose a hybrid supra-cycle number and hybrid supra-cycle ratio based on the cycle structure, and present an extensive experimental analysis by comparing our indexes and several different indexes in four real multiplex networks on layer nodes and multiplex nodes. The experimental results show that these proposed indexes have good robustness, synchronization, and transmission dynamics. Finally, we provide an in-depth understanding of multiplex networks and cycle structure, and we sincerely hope more valuable academic achievements are proposed in the future.

Robustness measurement of multiplex networks based on graph spectrum.

Networks can provide effective representations of the relationships between elements in complex systems through nodes and links. On this basis, relationships between multiple systems are often characterized as multilayer networks (or networks of networks). As a typical representative, a multiplex network is often used to describe a system in which there are many replaceable or dependent relationships among elements in different layers. This paper studies robustness measures for different types of multiplex networks by generalizing the natural connectivity calculated from the graph spectrum. Experiments on model and real multiplex networks show a close correlation between the robustness of multiplex networks consisting of connective or dependent layers and the natural connectivity of aggregated networks or intersections between layers. These indicators can effectively measure or estimate the robustness of multiplex networks according to the topology of each layer. Our findings shed new light on the design and protection of coupled complex systems.

Enhancing Robustness and Resilience of Multiplex Networks Against Node-Community Cascading Failures

Many real systems are represented in form of multiplex networks composed of a set of nodes, multiple layers of links, and coupling node relationships across all layers. These systems are very vulnerable to damages during both attacks and recoveries due to potential node cascading failures (NCFs). Although some progress has recently been made in studying network robustness and resilience, the comprehensive impacts of coupling node relationships and community structures on NCFs remain unclear. Accordingly, in this article, we study the robustness and resilience of multiplex networks in the presence of NCFs caused by coupling node relationships and community structures. We first model the failure processes of multiplex networks during both attacks and recoveries as node-community cascading failures (called NCCFs), and then theoretically demonstrate the fragility of multiplex networks to random node damages under NCCFs. Subsequently, to improve network robustness and resilience, we adopt a node protection strategy and propose a cost-aware constrained optimization problem. Finally, we devise a degree-based simulated annealing algorithm for solving this optimization problem. Extensive experiments on both simulated and real multiplex networks show that NCCFs make networks more vulnerable to unpredictable damage than classical NCFs. The results also show the superiority of the proposed algorithm over the state-of-the-art algorithms in improving network robustness and resilience.

Impact of Centrality Measures on the Common Neighbors in Link Prediction for Multiplex Networks.

Complex networks are representations of real-world systems that can be better modeled as multiplex networks, where the same nodes develop multi-type connections. One of the important concerns about these networks is link prediction, which has many applications in social networks and recommender systems. In this article, similarity-based methods such as common neighbors (CNs) are the mainstream. However, in the CN method, the contribution of each CN in the likelihood of new connections is equally taken into account. In this work, we propose a new link prediction method namely Weighted Common Neighbors (WCN), which is based on CNs and various types of Centrality measures (including degree, k-core, closeness, betweenness, Eigenvector, and PageRank) to predict the formation of new links in multiplex networks. So, in this model, each CN has a different impact on the node connection likelihood. Moreover, we investigate the impact of interlayer information on improving the performance of link prediction in the target layer. Using Area under the ROC Curve and precision as evaluation metrics, we perform a comprehensive experimental evaluation of our proposed method on seven real multiplex networks. The results validate the improved performance of our proposed method compared with existing methods, and we show that the performance of proposed methods is significantly improved while using interlayer information in multiplex networks.

Core-based Approach to Measure Pairwise Layer Similarity in Multiplex Network

Most of the recent works on network science are focused on investigating various interactions among a set of entities present in a system that can be represented by multiplex network. Each type of relationship is treated as a layer of multiplex network. Some of the recent works on multiplex networks are focused on deriving layer similarity from node similarity where node similarity is evaluated using neighborhood similarity measures like cosine similarity and Jaccard similarity. But this type of analysis lacks in finding the set of nodes having the same influence in both the network. The discovery of influence similarity between the layers of multiplex networks helps in strategizing cascade effect, influence maximization, network controllability, etc. Towards this end, this paper proposes a pairwise similarity evaluation of layers based on a set of common core nodes of the layers. It considers the number of nodes present in the common core set, the average clustering coefficient of the common core set, and fractional influence capacity of the common core set to quantify layer similarity. The experiment is carried out on three real multiplex networks. As the proposed notion of similarity uses a different aspect of layer similarity than the existing one, a low positive correlation (close to non-correlation) is found between the proposed and existing approach of layer similarity. The result demonstrates that the degree of coreness difference is less for the datasets in the proposed method than the existing one. The existing method reports the coreness difference to be 40% and 18.4% for the datasets CS-AARHUS and EU-AIR TRANSPORTATION MULTIPLEX respectively whereas it is found to be 20% and 8.1% using proposed approach.

K-core structure of real multiplex networks

The authors show that interlayer correlations are responsible for the strong k-core structure found in real world multiplex networks. The more heterogeneous are the degree distributions of the layers, the more pivotal is the role of degree correlations. The less heterogeneous are the degree distributions, the more crucial is the role of correlations at the level of node similarities. These findings may help in identifying influential spreaders in real world multiplex systems.

Link prediction in multiplex networks based on interlayer similarity

Some networked systems can be better modeled by multilayer structure where the individual nodes develop relationships in multiple layers. Multilayer networks with similar nodes across layers are also known as multiplex networks. This manuscript proposes a novel framework for predicting forthcoming or missing links in multiplex networks. The link prediction problem in multiplex networks is how to predict links in one of the layers, taking into account the structural information of other layers. The proposed link prediction framework is based on interlayer similarity and proximity-based features extracted from the layer for which the link prediction is considered. To this end, commonly used proximity-based features such as Adamic–Adar and Jaccard Coefficient are considered. These features that have been originally proposed to predict missing links in monolayer networks, do not require learning, and thus are simple to compute. The proposed method introduces a systematic approach to take into account interlayer similarity for the link prediction purpose. Experimental results on both synthetic and real multiplex networks reveal the effectiveness of the proposed method and show its superior performance than state-of-the-art algorithms proposed for the link prediction problem in multiplex networks.

Controlling the uncertain response of real multiplex networks to random damage

We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a poor metric of system robustness. We show instead that a large deviation approach to percolation provides a more accurate characterization of system robustness. We identify an effective percolation threshold at which we observe a clear abrupt transition separating two distinct regimes in which the most likely response to damage is either a functional or a dismantled multiplex network. We leverage our findings to propose a new metric, named safeguard centrality, able to single out the nodes that control the response of the entire multiplex network to random damage. We show that safeguarding the function of top-scoring nodes is sufficient to prevent system collapse.

Geometric Correlations Mitigate the Extreme Vulnerability of Multiplex Networks against Targeted Attacks

We show that real multiplex networks are unexpectedly robust against targeted attacks on high-degree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

Percolation in real multiplex networks.

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where nodes are present in the system with given probability. The approach relies on the locally treelike ansatz, so that it is expected to accurately reproduce the true percolation diagram of sparse multiplex networks with negligible number of short loops. The performance of our theory is tested in social, biological, and transportation multiplex graphs. When compared against previously introduced methods, we observe improvements in the prediction of the percolation diagrams in all networks analyzed. Results from our method confirm previous claims about the robustness of real multiplex networks, in the sense that the average connectedness of the system does not exhibit any significant abrupt change as its individual components are randomly destroyed.

Hidden geometric correlations in real multiplex networks

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.

Structure of triadic relations in multiplex networks

Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different ‘layers’ that each represent one of many possible subsystems or types of interactions. Nevertheless, it is traditional to aggregate multilayer networks into a single weighted network in order to take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic, as important information can be lost as a result. It is therefore important to develop multilayer generalizations of network concepts. In this paper, we analyze triadic relations and generalize the idea of transitivity to multiplex networks. By focusing on triadic relations, which yield the simplest type of transitivity, we generalize the concept and computation of clustering coefficients to multiplex networks. We show how the layered structure of such networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute multiplex clustering coefficients for several real multiplex networks and illustrate why one must take great care when generalizing standard network concepts to multiplex networks. We also derive analytical expressions for our clustering coefficients for ensemble averages of networks in a family of random multiplex networks. Our analysis illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. These insights are invisible if one only studies aggregated networks.