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2017 ; 7
(1
): 2142
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Shortest Paths in Multiplex Networks
#MMPMID28526822
Ghariblou S
; Salehi M
; Magnani M
; Jalili M
Sci Rep
2017[May]; 7
(1
): 2142
PMID28526822
show ga
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.