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Abstract The centrality of a position within a network of positions refers to its importance to the functioning of the network and/or the influence the position has on other positions within the network. The appropriate measure of centrality should depend on the process being studied, but there are scientific advantages to the use of a few standard measures.

There will be occasions in which a researcher wants to ignore some dyads in the computation of centrality in order to avoid biased or misleading results. This paper presents a principled way of computing eigenvector-like centrality scores when some dyads are not included in the calculations. (C) 2015 Elsevier B.V. All rights reserved.

This article uses Academy Award nominations for acting to explore how artistic achievement is situated within a collaborative context. Assessment of individual effort is particularly difficult in film because quality is not transparent, but the project-based nature of the field allows us to observe individuals in multiple collaborative contexts. We address these issues with analyses of the top-10 credited roles from films released in theaters between 1936 and 2005. Controlling for an actor's personal history and the basic traits of a film, we explore two predictions. First, we find that status, as measured by asymmetric centrality in the network of screen credits, is an efficient measure of star power and mediates the relationship between experience and formal artistic consecration. Second, we find that actors are most likely to be consecrated when working with elite collaborators. We conclude by arguing that selection into privileged work teams provides cumulative advantage.

This paper presents and tests a general model to predict emergent exchange patterns and power differences in reciprocal exchange networks when individual actors follow the norm of reciprocity. With an interesting qualification, the experimental results reported here support the power-dependence approach (Emerson 1972a, b): those who acquire the most resources are connected to others who are dependent on them for rewards. Although, as Molm has abundantly demonstrated (1999, 2000, 2001, 2007), the quality of the relationship in negotiated and reciprocal exchange networks is quite different, and the details of a general model of network exchange might well differ for negotiated and reciprocal exchange, experimental results presented here indicate that power in networks, no matter how complex, is linked to dependence regardless of whether actors are motivated by rational choice or a norm of reciprocity

to build accurate models of relational data. Carter Butts discusses the conditions under which simple distance is a major predictor of total network structure in large and spatially embedded networks. Peter Hoff sets out a generalized linear mixed effects approach to modeling social networks in which depen dence among ties is attributed to unobserved attributes of vertices, which relate preferen tially to vertices with similar attribute values. Michael Ward, Peter Hoff, and Corey Lofdahl give an extended application of Hoff's mod eling approach to international relations among Central Asian countries with specific attention given to how the analysis can be used to impute missing network linkages. Finally, Nosh Contractor and Peter Monge's chapter reviews theories and theoretical mechanisms that have been proposed to gov em the formation of relations and embeds that review in a multi-theoretical, multi-level mod eling approach focused on networks of orga nizations that compete for similar resources (adversarial networks). It is worth noting that the workshop was held in 2002 and the edited volume of papers published in 2003. Research since then has advanced along many of the fronts discussed in the papers, in particular, the statistical mod eling of networks using exponential random graph models. Nevertheless, the volume remains valuable as an overview of a wide ranging set of research concerns that com poses the field of modern social network analysis. At the same time, the Office of Naval Research got its money's worth: there were papers that specifically addressed questions driven by national security concerns and the final comments by Kathleen Carley set out a clear road map by which social network analysis could better contribute to the solution of national security problems, providing new tools and techniques of analysis and, just as important, clear understanding of their limita tions in field situations.

Eigenvectors, and the related centrality measure Bonacich's c(β), have advantages over graph-theoretic measures like degree, betweenness, and closeness centrality: they can be used in signed and valued graphs and the beta parameter in c(β) permits the calculation of power measures for a wider variety of types of exchange. Degree, betweenness, and closeness centralities are defined only for classically simple graphs—those with strictly binary relations between vertices. Looking only at these classical graphs, where eigenvectors and graph–theoretic measures are competitors, eigenvector centrality is designed to be distinctively different from mere degree centrality when there are some high degree positions connected to many low degree others or some low degree positions are connected to a few high degree others. Therefore, it will not be distinctively different from degree when positions are all equal in degree (regular graphs) or in core-periphery structures in which high degree positions tend to be connected to each other.

Many social transactions are supra-dyadic; they either involve more than two participants (buyer, seller, broker) or they involve important aspects of the interaction's setting, tike its timing or its location. Standard network techniques do not adequately plumb these networks. Using the concept of a hypergraph [Berge, C. 1973, Graphs and Hypergraphs], this paper shows how the concept of network centrality can be adapted to supra-dyadic networks. Use of the technique is illustrated with data on attacks by inhabitants of Caribbean islands on Spanish settlements in the period 1509–1700.

A new measure of status or network centrality that takes into account both positive and negative relationships is suggested. This measure is based on the eigenvector measure of centrality, a standard measure in network research. Its use is illustrated with data from Sampson's well-known study of monks in a monastery.

Cellular automata (CA) can be used in simulations of network processes and network evolution by identifying adjacent vertices in a network with neighboring cells in a CA. However, there are restrictions on networks that can be represented by two dimensional CAs. For example, the degree of a vertex, the maximum number of unconnected neighbors, and the maximum size of a clique, are limited. Moreover, a high degree of transitivity is built into the two dimensional CA.Increasing the number of dimensions beyond two relaxes all the constraints. Moreover, the reduced transitivity of higher dimensional CAs allows us to vary in a systematic way the "localness "of the connections. Thus, we can examine the differences between strong (local and transitive) versus weak (non-transitive) ties, a difference that Granovetter and others have shown to be important. The paper offers equations describing how maximum degree, maximum clique size, maximum number of unconnected neighbors, and transitivity vary with the dimensions of the CA.

We consider a discrete time Markov chain whose state space is the set of all N×N stochastic matrices with zero diagonal entries. This chain models the evolution of relationships among N individuals who exchange gifts according to probabilities determined by previous exchanges. We determine the stable equilibria for this chain, and prove convergence to a mixture of these. In particular, we show that for generic initial states, the chain converges to a randomly chosen set of constellations made up of disjoint stars. Each star has a center, which is the recipient of all gifts from the other individuals in that star, while the center distributes his gifts only to members of his own star.

Network centrality is thought to be crucial for the efficient distribution of information or resources through a social network. Inherent to this structure, the flow of information in high-centrality networks can be easily undermined. By introducing two concepts, network efficiency and vulnerability, we show that efficiency is compromised more in networks characterized by high degree centralization when degree and betweenness centrality are not distinct than in other networks, following the removal of network positions. Vulnerability is the loss in efficiency resulting from the elimination of nodes. The resiliency of a network was then assessed following, progressive removal of nodes and all adjacent nodes. Nodes were removed in two ways: 1) randomly, which modeled incidental vulnerability; or, 2) based on the calculated centrality measures, which modeled vulnerability to a strategic attack. Our findings highlight the social impact of removing a person from a network, which is likely to disable, or make inactive, all direct ties to that individual. Such network analyses can be used to undermine or fortify existing network structures necessary for law enforcement and those concerned with national security.

Eigenvectors of adjacency matrices are useful as measures of centrality or of status. However, they are misapplied to asymmetric networks in which some positions are unchosen. For these networks, an alternative measure of centrality is suggested that equals an eigenvector when eigenvectors can be used and provides meaningfully comparable results when they cannot.