Nodes In Multiplex Networks Research Articles

Identifying top influential spreaders based on the influence weight of layers in multiplex networks

Detecting influential nodes in multiplex networks is a complex task due to the presence of multiple layers. In this study, we propose a method for identifying important layers with strong spreaders based on several key parameters. These include a layer's position within a well-connected neighborhood, the number of active edges and critical nodes, the ratio of active nodes to all possible connections, and the intersection of intra-layer communication compared to other layers. To accomplish this, we have formulated a layer weighting method which takes into account these parameters, and developed an algorithm for mapping and computing the rank of nodes based on their spreading capability within multiplex networks. The resulting layer weighting is then used to map and compress centrality vector values to a scalar value, allowing us to calculate node centrality in multiplex networks via a coupled set of equations. Moreover, our method combines the important layer parameters to compute the influence of nodes from different layers. Our experimental results, conducted on both synthetic and real-world networks, demonstrate that the proposed approach significantly outperforms existing methods in detecting high influential spreaders. These findings highlight the importance of using a suitable layer weighting measure for identifying potential spreaders in multiplex networks.

Target Controllability in Multilayer Networks via Minimum-Cost Maximum-Flow Method.

In this article, to maximize the dimension of controllable subspace, we consider target controllability problem with maximum covered nodes set in multiplex networks. We call such an issue as maximum-cost target controllability problem. Likewise, minimum-cost target controllability problem is also introduced which is to find minimum covered node set and driver node set. To address these two issues, we first transform them into a minimum-cost maximum-flow problem based on graph theory. Then an algorithm named target minimum-cost maximum-flow (TMM) is proposed. It is shown that the proposed TMM ensures the target nodes in multiplex networks to be controlled with the minimum number of inputs as well as the maximum (minimum) number of covered nodes. Simulation results on Erdős-Rényi (ER-ER) networks, scale-free (SF-SF) networks, and real-life networks illustrate satisfactory performance of the TMM.

Cluster-based topological features of nodes in a multiplex network—from a network of networks perspective

In the gathered multiplex systems, nodes inherit a part of their original system’s topological features, as in the world economic system, national policies and resource distribution bring industry advantages and resource advantages to the domestic industry. Although they represent one of the important original topological features of nodes, the inherited topological features of nodes have not received sufficient attention and have hardly been analyzed by existing network models. In our research, we defined the inherited topological features of nodes as ‘cluster-based topological features. To accurately calculate the cluster-based topological features of nodes in multiplex networks, we first provide a network model to summarize the multiplex networks into a calculable network of networks (NoN). Based on our network model, we propose a series of algorithms for calculating industries’ cluster-based topological features. Our calculating process contains 2 steps: ‘abstracting’ the NoN into one-layer calculable network; ‘inheriting’ subnetworks’ topological features into the inner nodes. Our network model and calculation algorithms are applied in a series of theoretical and empirical multiplex networks. The results not only confirm the realizability of our model but also produce several interesting findings, the most important of which is that some unremarkable nodes in multiplex network may have a very high contributory value from NoN perspective.

An Eigenvector Centrality for Multiplex Networks with Data

Networks are useful to describe the structure of many complex systems. Often, understanding these systems implies the analysis of multiple interconnected networks simultaneously, since the system may be modelled by more than one type of interaction. Multiplex networks are structures capable of describing networks in which the same nodes have different links. Characterizing the centrality of nodes in multiplex networks is a fundamental task in network theory. In this paper, we design and discuss a centrality measure for multiplex networks with data, extending the concept of eigenvector centrality. The essential feature that distinguishes this measure is that it calculates the centrality in multiplex networks where the layers show different relationships between nodes and where each layer has a dataset associated with the nodes. The proposed model is based on an eigenvector centrality for networks with data, which is adapted according to the idea behind the two-layer approach PageRank. The core of the centrality proposed is the construction of an irreducible, non-negative and primitive matrix, whose dominant eigenpair provides a node classification. Several examples show the characteristics and possibilities of the new centrality illustrating some applications.

Centrality ranking in multiplex networks using topologically biased random walks

Abstract Characterizing the statistically significant centrality of nodes is one of the main goals of multiplex networks. However, current centrality measures for node rankings focus only on either random walks or on the topological structure of the network. A pressing challenge is how to measure centrality of nodes in multiplex networks, depending both on network topology and on the biased types of random walks, such as the biased walks dealing with the properties of each node separately at each layer, or the biased walks considering instead one or even more intrinsically multiplex properties of the arrival node. In the paper, considering these two aspects, we propose a mathematical framework based on topologically biased random walk, called topologically biased multiplex PageRank, which allows to calculate centrality and accordingly rank nodes in multiplex networks. In particular, depending on the nature of biases and the interaction of nodes between different layers, we distinguish additive, multiplicative and combined cases of topologically biased multiplex PageRank. Each case by tuning the bias parameters reflects how the centrality ranking of a node in one layer affects the ranking its replica can gain in the other layers, and captures the extent to which the walkers preferentially visit hubs or poorly connected nodes. Experiments on two real-world multiplex networks show that the topologically biased multiplex PageRank outperforms both its corresponding unbiased case and the current ranking methods, and it can efficiently capture the significantly top-ranked nodes in multiplex networks by means of a proper tuning of the biases in the walks.

Multiple resource demands and viability in multiplex networks.

Many complex systems demand manifold resources to be supplied from distinct channels to function properly, e.g., water, gas, and electricity for a city. Here, we study a model for viability of such systems demanding more than one type of vital resource be produced and distributed by resource nodes in multiplex networks. We found a rich variety of behaviors such as discontinuity, bistability, and hysteresis in the fraction of viable nodes with respect to the density of networks and the fraction of resource nodes. Our result suggests that viability in multiplex networks is not only exposed to the risk of abrupt collapse but also suffers excessive complication in recovery.

Multiplex PageRank

Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social networks where people are involved in different types of relationships and interact through various forms of communication media. The ranking of nodes in multiplex networks is one of the most pressing and challenging tasks that research on complex networks is currently facing. When pairs of nodes can be connected through multiple links and in multiple layers, the ranking of nodes should necessarily reflect the importance of nodes in one layer as well as their importance in other interdependent layers. In this paper, we draw on the idea of biased random walks to define the Multiplex PageRank centrality measure in which the effects of the interplay between networks on the centrality of nodes are directly taken into account. In particular, depending on the intensity of the interaction between layers, we define the Additive, Multiplicative, Combined, and Neutral versions of Multiplex PageRank, and show how each version reflects the extent to which the importance of a node in one layer affects the importance the node can gain in another layer. We discuss these measures and apply them to an online multiplex social network. Findings indicate that taking the multiplex nature of the network into account helps uncover the emergence of rankings of nodes that differ from the rankings obtained from one single layer. Results provide support in favor of the salience of multiplex centrality measures, like Multiplex PageRank, for assessing the prominence of nodes embedded in multiple interacting networks, and for shedding a new light on structural properties that would otherwise remain undetected if each of the interacting networks were analyzed in isolation.

Eigenvector centrality of nodes in multiplex networks

We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type centralities. In addition, we rigorously show that, under reasonable conditions, such centrality measures exist and are unique. Computer experiments and simulations demonstrate that the proposed measures provide substantially different results when applied to the same multiplex structure, and highlight the non-trivial relationships between the different measures of centrality introduced.