Spreading processes in Multilayer Networks

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.Comment: 21 pages, 3 figures, 4 table

Country centrality in the international multiplex network

Abstract In this work we introduce and analyze a new and comprehensive multilayer dataset covering a wide spectrum of international relationships between coutries. We select two cross sections of the dataset corresponding to years 2003 and 2010 with 19 layers and 112 nodes to study the structure and evolution of the network. Country centrality is measured by the multiplex PageRank (MultiRank) and the multiplex hub and authority scores (MultiHub and MultiAuth). We find that the MultiHub measure has the highest correlation to GDP per capita, with respect to the other multilayer measures and to their single layer analogues. Finally we analyze the differences in the ranking between GDP per capita and the multilayer centrality measures to evaluate them as measures of development

Eigenvector-Based Centrality Measures for Temporal Networks

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NTxNT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.Comment: 38 pages, 7 figures, and 5 table

Analysis of a Voting Method for Ranking Network Centrality Measures on a Node-aligned Multiplex Network

Identifying relevant actors using information gleaned from multiple networks is a key goal within the context of human aspects of military operations. The application of a voting theory methodology for determining nodes of critical importance—in ranked order of importance—for a node-aligned multiplex network is demonstrated. Both statistical and qualitative analyses on the differences of ranking outcomes under this methodology is provided. As a corollary, a multilayer network reduction algorithm is investigated within the context of the proposed ranking methodology. The application of the methodology detailed in this thesis will allow meaningful rankings of relevant actors to be produced on a multiplex network

The Whole Is Greater than the Sum of the Parts: A Multilayer Approach on Criminal Networks

Traditional social network analysis can be generalized to model some networked systems by multilayer structures where the individual nodes develop relationships in multiple layers. A multilayer network is called multiplex if each layer shares at least one node with some other layer. In this paper, we built a unique criminal multiplex network from the pre-trial detention order by the Preliminary Investigation Judge of the Court of Messina (Sicily) issued at the end of the Montagna anti-mafia operation in 2007. Montagna focused on two families who infiltrated several economic activities through a cartel of entrepreneurs close to the Sicilian Mafia. Our network possesses three layers which share 20 nodes. The first captures meetings between suspected criminals, the second records phone calls and the third detects crimes committed by pairs of individuals. We used measures from multilayer network analysis to characterize the actors in the network based on their local edges and their relevance to each specific layer. Then, we used measures of layer similarity to study the relationships between different layers. By studying the actor connectivity and the layer correlation, we demonstrated that a complete picture of the structure and the activities of a criminal organization can be obtained only considering the three layers as a whole multilayer network and not as single-layer networks. Specifically, we showed the usefulness of the multilayer approach by bringing out the importance of actors that does not emerge by studying the three layers separately

An extended approach of weight collective influence graph for detection influence actor

Over the last decade, numerous methods have been developed to detect the influential actors of hate speech in social networks, one of which is the Collective Influence (CI) method. However, this method is associated with unweighted datasets, which makes it inappropriate for social media, significantly using weight datasets. This study proposes a new CI method called the Weighted Collective Influence Graph (WCIG), which uses the weights and neighbor values to detect the influence of hate speech. A total of 49, 992 Indonesian tweets were and extracted from Indonesian Twitter accounts, from January 01 to January 22, 2021. The data collected are also used to compare the results of the proposed WCIG method to determine the influential actors in the dissemination of information. The experiment was carried out two times using parameters ∂=2 and ∂=4. The results showed that the usernames bernacleboy and zack_rockstar are influential actors in the dataset. Furthermore, the time needed to process WCIG calculations on HPC is 34-75 hours because the larger the parameter used, the greater the processing time