Abstract
Real networks are heterogeneous structures, with edges unevenly distributed among nodes, presenting community structure, motifs, transitivity, rich clubs, and other kinds of topological patterns. Consequently, the roles played by nodes in a network can differ greatly. For example, some nodes may be connectors between parts of the network, others may be central or peripheral, etc. The objective of this chapter is to describe how we can find the most important nodes in networks. The idea is to define a centrality measure for each node in the network, sort the nodes according to their centralities, and fix our attention to the first ranked nodes, which can be considered as the most relevant ones with respect to this centrality measure.
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Notes
- 1.
In some texts the adjacency matrix is defined in the opposite direction, i.e., a ij is used to encode an edge from node j to node i, for example, in [44]. This is an important issue to care about when dealing with directed networks.
- 2.
Network of Thrones: https://www.macalester.edu/~abeverid/thrones.html.
- 3.
Pajek: http://mrvar.fdv.uni-lj.si/pajek.
- 4.
Gephi: https://gephi.org.
- 5.
Radatools: http://deim.urv.cat/~sergio.gomez/radatools.php.
- 6.
Cytoscape: http://www.cytoscape.org.
- 7.
igraph: http://igraph.org.
- 8.
NetworkX: http://networkx.github.io.
- 9.
- 10.
Visone: https://www.visone.info.
- 11.
MuxViz: http://muxviz.net.
- 12.
graph-tool: https://graph-tool.skewed.de.
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Acknowledgements
S.G. acknowledges funding from the Spanish Ministerio de Economía y Competitividad (grant number FIS2015-71582-C2-1).
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Gómez, S. (2019). Centrality in Networks: Finding the Most Important Nodes. In: Moscato, P., de Vries, N. (eds) Business and Consumer Analytics: New Ideas. Springer, Cham. https://doi.org/10.1007/978-3-030-06222-4_8
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