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Journal ArticleDOI

Power and Centrality: A Family of Measures

01 Mar 1987-American Journal of Sociology (University of Chicago Press)-Vol. 92, Iss: 5, pp 1170-1182
TL;DR: In this article, the rank orderings by the four networks whose analysis forms the heart of this paper were analyzed and compared to the rank ordering by the three centrality measures, i.e., betweenness, nearness, and degree.
Abstract: 2In an influential paper, Freeman (1979) identified three aspects of centrality: betweenness, nearness, and degree. Perhaps because they are designed to apply to networks in which relations are binary valued (they exist or they do not), these types of centrality have not been used in interlocking directorate research, which has almost exclusively used formula (2) below to compute centrality. Conceptually, this measure, of which c(ot, 3) is a generalization, is closest to being a nearness measure when 3 is positive. In any case, there is no discrepancy between the measures for the four networks whose analysis forms the heart of this paper. The rank orderings by the
Citations
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Journal ArticleDOI
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

17,647 citations

Journal ArticleDOI
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

9,441 citations

Journal ArticleDOI
TL;DR: A thorough exposition of community structure, or clustering, is attempted, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists.
Abstract: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

9,057 citations

Journal ArticleDOI
TL;DR: A thorough exposition of the main elements of the clustering problem can be found in this paper, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

8,432 citations

Book
30 Dec 1991
TL;DR: In this article, the development of social network analysis, tracing its origins in classical sociology and its more recent formulation in social scientific and mathematical work, is described and discussed. But it is argued that the analysis of social networks is not a purely static process.
Abstract: This paper reports on the development of social network analysis, tracing its origins in classical sociology and its more recent formulation in social scientific and mathematical work. It is argued...

6,366 citations

References
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Book
01 Jan 1983

34,729 citations

Journal ArticleDOI
TL;DR: In this article, three distinct intuitive notions of centrality are uncovered and existing measures are refined to embody these conceptions, and the implications of these measures for the experimental study of small groups are examined.

14,757 citations

Journal ArticleDOI
TL;DR: A new method of computation which takes into account who chooses as well as how many choose is presented, which introduces the concept of attenuation in influence transmitted through intermediaries.
Abstract: For the purpose of evaluating status in a manner free from the deficiencies of popularity contest procedures, this paper presents a new method of computation which takes into accountwho chooses as well ashow many choose. It is necessary to introduce, in this connection, the concept of attenuation in influence transmitted through intermediaries.

3,386 citations

Journal ArticleDOI
TL;DR: In this paper, Factoring and weighting approaches to status scores and clique identification were proposed, and the results showed that the weighting approach is more accurate than the factoring approach.
Abstract: (1972). Factoring and weighting approaches to status scores and clique identification. The Journal of Mathematical Sociology: Vol. 2, No. 1, pp. 113-120.

2,661 citations


"Power and Centrality: A Family of M..." refers background in this paper

  • ...I have proposed (Bonacich 1972a, 1972b) a measure of centrality (in this paper, I will call it "e") in which a unit's centrality is its summed connections to others, weighted by their centralities....

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