Abstract
We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone. We apply this methodology to the empirical multiplex lexical network encoding the linguistic relationships known to English speaking toddlers. We show that the distance entropy cartography better predicts how children learn words compared to closeness centrality. Our results highlight the importance of distance entropy for gaining insights from distance patterns in complex networks.
Highlights
Network science provides a powerful framework for modelling and understanding how individual entities give rise to complex—and often unexpected—phenomena by interacting with each other [1,2,3,4,5,6]
By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone
We introduce a new type of distance entropy, characterising the distribution of path lengths from a given node in a network
Summary
Network science provides a powerful framework for modelling and understanding how individual entities give rise to complex—and often unexpected—phenomena by interacting with each other [1,2,3,4,5,6]. Defining the centrality of nodes in complex networks is an important question for determining the role of individual agents in a variety of dynamical processes such as information flow and influence maximisation [7,8,9], network growth [1], and resilience to cascade failures [10,11]. In many of these processes, centrality can be defined by means of network distance—that is, the minimum number of links separating any two nodes. Our results provide compelling evidence for the importance of considering information measures relative to shortest paths for gaining insights into real-world complex systems
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