Abstract
Weighted networks have been extensively studied because they can represent various phenomena in which the diversity of edges is essential. To investigate the properties of weighted networks, various centrality measures have been proposed, such as strength, weighted clustering coefficients, and weighted betweenness centrality. In such measures, only direct connections or entire network connectivity from arbitrary nodes have been used to calculate the connectivity of each node. However, in weighted networks composed of autonomous elements such as humans, middle ranges from each node are also considered to be meaningful for characterizing each node’s connectability. In this study, we define a new node property in weighted networks to consider connectability to nodes within a range of two degrees of separation, then apply this new centrality to face-to-face human communication networks in corporate organizations. Our results show that the proposed centrality distinguishes inherent communities corresponding to the job types in each organization with a high degree of accuracy. This indicates the possibility that connectability to nodes within two degrees of separation reveals potential trends of weighted networks that are not apparent from conventional measures.
Highlights
Weighted networks have been extensively studied because they can represent various phenomena in which the diversity of edges is essential
Only direct connections or entire network connectivity from arbitrary nodes have been used to calculate the connectivity of each node
In weighted networks composed of autonomous elements such as humans, middle ranges from each node are considered to be meaningful for characterizing each node’s connectability
Summary
Weighted networks have been extensively studied because they can represent various phenomena in which the diversity of edges is essential. Network analysis is a useful method for analysing the structure of many-body systems from a topological viewpoint1 In this form of analysis, a many-body system is mathematically represented by a simple network composed of elements (nodes) and connections (edges) between elements. Various centrality measures ( “centralities”) for weighted networks have been proposed to investigate the properties of weighted networks, for example strength, weighted clustering coefficients, and weighted betweenness centrality7–9 When such centralities are included in the analysis, it becomes possible to reveal the relationship between weights and topology. One typical form of analysis investigates the relationship between degree and strength, each of which represents the number of the edges connected to each node and the sum of the weights assigned to them This relationship reveals interesting trends in weighted networks. No single node predetermines the structure of network connections over the entire www.nature.com/scientificreports/
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