2431. Edge-clustering coefficient in directed networks
Invited abstract in session TA-9: Statistical methods for finance, stream OR in Finance and Insurance .
Tuesday, 8:30-10:00Room: Clarendon SR 2.01
Authors (first author is the speaker)
| 1. | Giorgio Rizzini
|
| Department of Economics and Management, University of Brescia | |
| 2. | Rosanna Grassi
|
| Dep.t of Statistics and Quantitative Methods, Universita Milano-Bicocca |
Abstract
Clustering coefficient, that describes the triadic relations between nodes, is one of the most important structural indicators in network theory. Although many works are devoted to study the issue by a vertex perspective, a study by the point of view of the edge has not analysed enough. The aim of this work is to provide a new edge-clustering coefficient for unweighted directed networks, in line with the local clustering coefficient for nodes. We define the edge-clustering coefficient as the ratio between the actual triangles to which an edge belongs and all potential ones, that is, all triangles an edge could belong to. This coefficient captures the importance of the edges forming triadic relations among nodes highlighting the relevance of an edge within the network. We propose a closed-form formula to compute the edge-clustering coefficient based on the degrees of the edge endpoints. The extension of the coefficient to the directed case allows considering also the direction of the edges so that we are able to analyse different patterns of triangles constructed on each link. In this way, it is also possible to assess the strategic role of each edge in the transmission of any kind of relevant information. A detailed numerical analysis based on simulated and real networks shows how the proposal could provide meaningful insights into capturing at local level the topological structure of the network.
Keywords
- Graphs and Networks
- Social Networks
- Network Flows
Status: accepted
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