Experimental results on both synthetic and real-world HoMLN datasets demonstrate that the heuristics achieve accuracy comparable to the ground truth while significantly improving computational efficiency, thereby establishing the scalability and effectiveness of the HoMLN algorithms developed using the decoupling approach.
Abstract
Centrality measures are defined for simple graphs -- directed, undirected, weighted or unweighted. Attributed graphs have to be reduced to simple graphs for computing centrality measures. However, when applications with multiple types of relationships are modeled using multilayer networks (MLNs), simple graph algorithms cannot be directly used. Existing approaches typically analyze MLNs by aggregating layers of an MLN into a single graph, which results in the loss of structural and semantic information. The semantic information loss can be more pronounced particularly, in weighted networks. This work focuses on computing degree centrality in weighted homogeneous multilayer networks (HoMLNs) using a decoupling-based framework. The framework performs independent layer-wise analysis on MLNs without reducing them to simple graphs. The decoupling approach allows use of exiting algorithms for each layer and uses minimal information from individual layers for computing degree centrality of HoMLNs. We propose heuristic-based algorithms that strike a balance between accuracy and efficiency. The proposed methods are evaluated against ground truth (GT) results obtained using Boolean OR aggregation and naive baselines. Experimental results on both synthetic and real-world HoMLN datasets demonstrate that the heuristics achieve accuracy comparable to the ground truth while significantly improving computational efficiency, thereby establishing the scalability and effectiveness of the HoMLN algorithms developed using the decoupling approach.
The Influence-Spreading Model (ISM) introduces three probabilistic centrality measures: out-centrality, in-centrality, and ISM betweenness centrality. Out-centrality measures the average probability that a node influences others, while in-centrality measures the average probability that others influence a node. ISM betweenness centrality measures the change in total probabilistic influence when a node is removed. These measures depend on edge transmission probabilities and allow walks up to a specified maximum length. We compare the ISM centrality measures to commonly used weighted variants of out-degree, in-degree, closeness, shortest-path betweenness, and Katz centrality in directed, weighted networks using four real-world online social networks and nine synthetic networks generated by Erd\H{o}s-R\'enyi, navigable small-world, and directed scale-free models. For the synthetic networks, the edge probabilities are drawn from three beta distributions. We evaluate the similarity in centrality values and their ranking using Pearson correlation and Spearman's rank correlation coefficients. Results show strong correlations between the ISM out-centrality and weighted out-degree and outward Katz centrality, particularly for low edge probabilities. Conversely, relationships between the ISM in-centrality and other measures vary with network topology, sometimes yielding negative correlations. Correlations between the ISM betweenness and the shortest-path betweenness are also topology-dependent and weaken as alternative influence paths become more relevant. Overall, standard centrality measures can approximate the influence of broadcasting influence but often miss the nuances of receiving influence and probabilistic intermediary roles.
Temporal networks offer a suitable representation for complex systems in which interactions vary over time, such as communication, transportation, and social networks. Identifying influential nodes in such networks is more challenging than in static graphs because node importance depends not only on network structure but also on the timing and ordering of interactions. Although many temporal centrality measures have been proposed, the literature remains fragmented, with limited consensus on their comparative performance and applicability. This paper presents a critical and comparative survey of centrality measures in temporal networks. We review both temporal extensions of classical centrality metrics and measures specifically designed for temporal graphs, and propose a functional taxonomy that categorizes existing approaches according to the primary mechanism through which influence is quantified in temporal networks. The proposed taxonomy organizes temporal centrality measures into interaction-based, path-based, walk-based, spectral-based and robustness-based categories, providing a unified perspective on their underlying principles. In addition, we provide comparative insights to help select appropriate temporal centrality measures under different network characteristics and application settings. To complement the survey, we conduct experiments on multiple real-world temporal network datasets. The measures are evaluated through influence spreading experiments using epidemic diffusion models, ranking consistency analysis based on Kendall's rank correlation, and runtime complexity analysis to assess computational efficiency and scalability. Finally, we highlight key open challenges and future research directions, including scalability for million-sized networks and the need for standardized evaluation frameworks.
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