A Faster Katz Status Score Algorithm

A new graph theoretical algorithm to calculate Katz status scores reduces computational complexity from time O(n3) to O(n + m). Randomly-generated graphs as well as data from a large empiric study are used to test the performance of two commercial network analysis packages (GRADAP and UCINET V), compared to the performance achieved by the authors' algorithm, implemented in Visual Basic.

[1]  Forman S. Acton,et al.  Numerical methods that work , 1970 .

[2]  Á. M. Hernáez.  Borgatti, Stephen; Martin Everett i Lin Freeman. UCINET IV. Network Analysis Software. Version 1.0. Columbia: Analytic Technologies, 1992 , 1995 .

[3]  U. Brandes.  Faster Evaluation of Shortest-Path Based Centrality Indices , 2000 .

[4]  Noah E. Friedkin,et al.  Theoretical Foundations for Centrality Measures , 1991, American Journal of Sociology.

[5]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[6]  Craig Stinson,et al.  Running Microsoft Windows NT Workstation, Version 4 , 1991 .

[7]  Richard Rothenberg,et al.  Choosing a centrality measure: Epidemiologic correlates in the Colorado Springs study of social networks☆ , 1995 .

[8]  S Q Muth,et al.  Social networks in disease transmission: the Colorado Springs Study. , 1995, NIDA research monograph.

[9]  P. Bonacich.  Factoring and weighting approaches to status scores and clique identification , 1972 .

[10]  Naomi Rosenthal,et al.  Centrality Analysis for Historians , 1987 .

[11]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[12]  Andrew Seary,et al.  Eigen Analysis of Networks , 2000, J. Soc. Struct..

[13]  M. Zelen,et al.  Rethinking centrality: Methods and examples☆ , 1989 .

[14]  R. Rothenberg,et al.  Social network dynamics and HIV transmission , 1998, AIDS.

[15]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[16]  J. Nash.  Compact Numerical Methods for Computers , 2018 .

[17]  Alden S. Klovdahl,et al.  Mapping a social network of heterosexuals at high risk for HIV infection , 1994, AIDS.