Visualization of a directed network with focus on its hierarchy and circularity

Yuichi Kichikawa (), Takashi Iino, Hiroshi Iyetomi and Hiroyasu Inoue ()
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Yuichi Kichikawa: Niigata University
Takashi Iino: Niigata University
Hiroshi Iyetomi: Niigata University

Journal of Computational Social Science, 2019, vol. 2, issue 1, No 3, 15-23

Abstract: Abstract The spring-electric model is a useful tool to visualize a large-scale complex network. However, information on the flow of directed network may not be properly reflected because links are basically treated as undirected. Here, we propose a new visualization method with an explicit account of network flow structure information by combining Helmholtz–Hodge decomposition and the spring-electric model. We then demonstrate its effectiveness by adopting actual Japanese production flow network as a test ground. The Helmholtz–Hodge decomposition enables us to break down flow on a directed network into two flow components: potential flow and circular flow. The potential flow between a pair of nodes is given by difference of their potentials, and hence, the potential of a node shows its hierarchical position in a network. On the other hand, the circular flow component illuminates feedback loops built in a network. We also identify dominant clusters of firms forming feedback loops by applying a flow-based community detection method to the extracted circular flow network. We find that both hierarchical and loop structures coexist within the major industries such as construction, manufacturing, and wholesales.

Keywords: Visualization; Directed graph; Helmholtz–Hodge decomposition; Community detection; Puroduction network (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s42001-019-00031-1

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