Abstract
The shortest path problem is one of the most fundamental networks optimization problems. Nowadays, individuals interact in extraordinarily numerous ways through their offline and online life (e.g., co-authorship, co-workership, or retweet relation in Twitter). These interactions have two key features. First, they have a heterogeneous nature, and second, they have different strengths that are weighted based on their degree of intimacy, trustworthiness, service exchange or influence among individuals. These networks are known as multiplex networks. To our knowledge, none of the previous shortest path definitions on social interactions have properly reflected these features. In this work, we introduce a new distance measure in multiplex networks based on the concept of Pareto efficiency taking both heterogeneity and weighted nature of relations into account. We then model the problem of finding the whole set of paths as a form of multiple objective decision making and propose an exact algorithm for that. The method is evaluated on five real-world datasets to test the impact of considering weights and multiplexity in the resulting shortest paths. As an application to find the most influential nodes, we redefine the concept of betweenness centrality based on the proposed shortest paths and evaluate it on a real-world dataset from two-layer trade relation among countries between years 2000 and 2015.
Highlights
Individuals are connected to one other through different interactions such as friendship, conversation, cooperation, and game
We name these paths as influential Pareto paths
We focus on the problem of finding shortest paths in multiplex networks, a generic term that we use to refer to a number of network models involving multiple types of relationships
Summary
Individuals are connected to one other through different interactions such as friendship, conversation, cooperation, and game. Most of the previous efforts on finding the distance between individuals are based on the degree of separation in single-layer networks (without considering the strength of relations and multiplexity)[19, 20]. In previous work[22], we introduced a geodesic distance named Pareto distance to deal with this heterogeneity, but the weighted nature of relations was ignored in that work which may result in non-optimal paths (for an example of finding optimal paths in multiplex networks in presence and absence of influence of relations refer to Supplementary Note 4). Influential Pareto distance uses the concept of Pareto efficiency and attempts at finding the paths in a multiplex network which have the optimal total weight (e.g., the maximum influence) in each layer separately. We redefined the concept of betweenness centrality based on these paths
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