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When Linton C. Freeman made his conceptual clarifications about centrality measures in social network analysis in 1979 he exclusively focused on unweighted, symmetric, and connected networks without the possibility of self-loops. Even though a lot of articles have been published in the last years discussing network measures for weighted, asymmetric or unconnected networks, the vast majority of researchers dealing with social network data simplify their networks based on Freeman's 1979 definitions before they calculate centrality measures. When dealing with weighted and/or asymmetric networks which can have self links and consist of multiple components, researchers are confronted with a lack of standardization. Different tools for social network analysis treat specific cases differently. In this article we describe and discuss the ways the software ORA (developed by CASOS at Carnegie Mellon University) handles the most important network measures in case of weighted, asymmetric, self-looped, and disconnected networks. In the center of our attention are the following measures, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, and clustering coefficient., Center for the Computational Analysis of Social and Organizational Systems (CASOS) technical report.

The ORA components are a collection of java executable programs for use in Social Network Analysis applications. These components are used by interface programs such as ORA GUI and SORASCS. The components described in this manual are based on the ORA v1.9.5.4.5 (August 2009) software release., Sponsored in part by the Air Force Office of Sponsored Research (MURI) and George Mason University under Grant No. 600322GRGMASON, and by the Army Research Lab under Grant No. DAAD19-01-2-0009.