Encyclopedia of Graphs

This network represents 129 publications (vertices) and 613 citations (edges) pointing from the cited paper towards the citing paper. Line values are 1 or 2:

• 1 represents a regular citation,
• 2 represents double citations (these are possible if the citing paper or the cited paper refers to two mutual citing papers shrunk to one combined vertex).

The original author is N.P.Hummon, with co-authors P. Doreian and L.C. Freeman.

Background:

In 1979, Linton Freeman published a paper which defined several kinds of centrality. His typology has become the standard for network analysis. Freeman, however, was not the first to publish on centrality in networks. His paper is part of a discussion which dates back to the 1940s. The network shows the papers that discuss network centrality and their cross- references until 1979.

In principle, papers can only cite papers which appeared earlier, so the network is acyclic. Arcs never point back to older papers just like parents cannot be younger than their children. However, there are usually some exceptions in a citation network: papers which cite one another, e.g., papers appearing at about the same time and written by one author. We eliminated these exceptions by shrinking the papers by an author which are connected by cyclic citations. In the centrality literature network, we used the latter approach (e.g., two publications by Gilch in 1954 are shrunk to one paper #GilchSW-54).

Network image:

Edges colored in grey have the value 1 while edges colored in black have the value 2.

References:

• N.P. Hummon, P. Doreian, & L.C. Freeman, 'Analyzing the structure of the centrality-productivity literature created between 1948 and 1979' (in: Knowledge-Creation Diffusion Utilization, 11 (1990), 459-480).
• W. de Nooy, A. Mrvar, & V. Batagelj, Exploratory Social Network Analysis with Pajek (Cambridge: Cambridge University Press, 2004), Chapter 11.

More information:

• https://sites.google.com/site/ucinetsoftware/datasets/centralityliteraturenetwork