A Critical Review of Centrality Measures in Social Networks

Social networks are currently gaining increasing impact in the light of the ongoing growth of web-based services like facebook.com. One major challenge for the economically successful implementation of selected management activities such as viral marketing is the identification of key persons with an outstanding structural position within the network. For this purpose, social network analysis provides a lot of measures for quantifying a member’s interconnectedness within social networks. In this context, our paper shows the state of the art with regard to centrality measures for social networks. Due to strongly differing results with respect to the quality of different centrality measures, this paper also aims at illustrating the tremendous importance of a reflected utilization of existing centrality measures. For this purpose, the paper analyzes five centrality measures commonly discussed in literature on the basis of three simple requirements for the behavior of centrality measures.

[1]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[2]  T. Valente.  Social network thresholds in the diffusion of innovations , 1996 .

[3]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[4]  Peter Mutschke,et al.  Zentralitätsanomalien und Netzwerkstruktur. Ein Plädoyer für einen „engeren“ Netzwerkbegriff und ein community-orientiertes Zentralitätsmodell , 2008 .

[5]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[6]  Martin Bichler,et al.  Identification of influencers - Measuring influence in customer networks , 2008, Decis. Support Syst..

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

[8]  Julia Heidemann,et al.  Online Social Networks – Ein sozialer und technischer Überblick , 2010, Informatik-Spektrum.

[9]  Jure Leskovec,et al.  Planetary-scale views on a large instant-messaging network , 2008, WWW.

[10]  S. Yook,et al.  Centrality measure of complex networks using biased random walks , 2009 .

[11]  Martin G. Everett,et al.  A Graph-theoretic perspective on centrality , 2006, Soc. Networks.

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

[13]  Berend Wierenga,et al.  Virtual communities: A marketing perspective , 2009, Decis. Support Syst..

[14]  J. Bolland,et al.  Sorting out centrality: An analysis of the performance of four centrality models in real and simulated networks , 1988 .

[15]  June Cotte,et al.  The Role of Network Centrality in the Flow of Consumer Influence , 2010 .

[16]  Alex Bavelas.  A Mathematical Model for Group Structures , 1948 .

[17]  René Algesheimer,et al.  A Network Based Approach to Customer Equity Management , 2006 .

[18]  P BorgattiStephen.  Identifying sets of key players in a social network , 2006 .

[19]  Thomas W. Valente,et al.  The stability of centrality measures when networks are sampled , 2003, Soc. Networks.

[20]  B. Wellman.  Structural analysis: From method and metaphor to theory and substance. , 1988 .

[21]  Stanley Milgram,et al.  An Experimental Study of the Small World Problem , 1969 .

[22]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[23]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M. A. Beauchamp.  AN IMPROVED INDEX OF CENTRALITY. , 1965, Behavioral science.

[25]  Detlef Schoder,et al.  Web Science 2.0: Identifying Trends through Semantic Social Network Analysis , 2008, 2009 International Conference on Computational Science and Engineering.

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

[27]  Shi Ying,et al.  Frontiers in Algorithmics , 2010, Lecture Notes in Computer Science.

[28]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[29]  Kees Niemöller,et al.  Applied network analysis , 1980 .

[30]  S. Bornholdt,et al.  Scale-free topology of e-mail networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Krishna P. Gummadi,et al.  Measurement and analysis of online social networks , 2007, IMC '07.

[32]  Croom Helm,et al.  Data Source: Scott, J. (1991). Social network analysis: A handbook. Newbury Park, California: SAGE Publications. , 1991 .

[33]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[34]  R. Langer,et al.  Where a pill won't reach. , 2003, Scientific American.

[35]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[36]  Dmitry Zinoviev,et al.  Toward Understanding Friendship in Online Social Networks , 2009, ArXiv.

[37]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[38]  Florian Probst,et al.  Valuation of online social networks taking into account users’ interconnectedness , 2010, Information Systems and e-Business Management.

[39]  Jure Leskovec,et al.  Worldwide Buzz: Planetary-Scale Views on an Instant-Messaging Network , 2007, WWW 2008.

[40]  J. Nieminen.  On the centrality in a graph. , 1974, Scandinavian journal of psychology.

[41]  Michel W. Barsoum,et al.  II. Experimental Results , 2001 .

[42]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[43]  Alexander Richter,et al.  Produkte zum IT-gestützten Social Networking in Unternehmen , 2007, Wirtschaftsinf..

[44]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[45]  M. E. Shaw.  Group Structure and the Behavior of Individuals in Small Groups , 1954 .

[46]  S. D. Berkowitz,et al.  Social Structures: A Network Approach , 1989 .

[47]  A. Graham.  Nonnegative matrices and applicable topics in linear algebra , 1987 .

[48]  Christian Stegbauer.  Netzwerkanalyse und Netzwerktheorie , 2008 .

[49]  Kon Shing Kenneth Chung,et al.  Exploring Temporal Communication Through Social Networks , 2007, INTERACT.

[50]  David A. Bader,et al.  Approximating Betweenness Centrality , 2007, WAW.

[51]  L. Freeman,et al.  Centrality in valued graphs: A measure of betweenness based on network flow , 1991 .

[52]  Vladimir Batagelj,et al.  Centrality in Social Networks , 1993 .

[53]  L. Freeman,et al.  Centrality in social networks: ii. experimental results☆ , 1979 .

[54]  D. Watts,et al.  An Experimental Study of Search in Global Social Networks , 2003, Science.

[55]  Stephen P. Borgatti,et al.  Identifying sets of key players in a social network , 2006, Comput. Math. Organ. Theory.

[56]  Lin Zhang,et al.  Betweenness centrality and Q-measures in directed valued networks , 2007, Scientometrics.

[57]  Ravi Kumar,et al.  Structure and evolution of online social networks , 2006, KDD '06.

[58]  Xiang-Yang Li,et al.  Ranking of Closeness Centrality for Large-Scale Social Networks , 2008, FAW.

[59]  Stephen P. Borgatti,et al.  Centrality and network flow , 2005, Soc. Networks.

[60]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .

[61]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[62]  Terrill L. Frantz,et al.  Robustness of centrality measures under uncertainty: Examining the role of network topology , 2009, Comput. Math. Organ. Theory.

[63]  Kathleen M. Carley,et al.  On the robustness of centrality measures under conditions of imperfect data , 2006, Soc. Networks.