Abstract
Network analysis naturally relies on graph theory and, more particularly, on the use of node and edge metrics to identify the salient properties in graphs. When building visual maps of networks, these metrics are turned into useful visual cues or are used interactively to filter out parts of a graph while querying it, for instance. Over the years, analysts from different application domains have designed metrics to serve specific needs. Network science is an inherently cross-disciplinary field, which leads to the publication of metrics with similar goals; different names and descriptions of their analytics often mask the similarity between two metrics that originated in different fields. Here, we study a set of graph metrics and compare their relative values and behaviors in an effort to survey their potential contributions to the spatial analysis of networks.
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Notes
- 1.
Strictly speaking, this requires that the graph does not have multiple edges, which is the case we consider here. Otherwise, paths should specify which edges are followed along the path.
- 2.
This being said, a random Erdős-Rényi graph might not be necessarily connected. For more details, see Bollobás (1985).
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Melançon, G., Rozenblat, C. (2013). Structural Analysis of Networks. In: Rozenblat, C., Melançon, G. (eds) Methods for Multilevel Analysis and Visualisation of Geographical Networks. Methodos Series, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6677-8_5
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