A note on actor network utilities and network evolution

The corrections provided by Xie and Cui [Xie, F., Cui, W., in press. Cost range and network structures. Social Networks, 30] to one of the theorems provided by Doreian [Doreian, P., 2006. Actor network utilities and network evolution. Social Networks, 28, 137–164] are both necessary and helpful. Accepting these corrections, and linking them more closely to the work of Hummon [Hummon, N.P., 2000. Utility and dynamic social networks. Social Networks, 22, 221–249], leads to some additional suggestions which, together with a restatement of some earlier results, help set the foundations for future work in this area.     

Cost range and the stable network structures

The work of this paper concerns with the stable structures in different cost range identified by Doreian in his paper [Doreian, P., 2006. Actor network utilities and network evolution. Social Networks 28, 137–164]. We point out some problems with his Theorem 4 and present our corrections to that theorem.     

Entropy as a measure of centrality in networks characterized by path-transfer flow

Recently, Borgatti [Borgatti, S.P., 2005. Centrality and network flow. Social Networks 27, 55–71] proposed a taxonomy of centrality measures based on the way that traffic flows through the network—whether over path, geodesic, trail, or walk, and whether by means of transfer, serial duplication, or parallel duplication. Most of the extant centrality measures assume that traffic propagates via parallel duplication or, alternatively, that it travels over geodesics. Few of the other flow possibilities have centrality measures associated with them. This article proposes an entropy-based measure of centrality appropriate for traffic that propagates by transfer and flows along paths. The proposed measure can be applied to most network types, whether binary or weighted, directed or undirected, connected or disconnected. The measure is illustrated on the gang alliance network of Kennedy et al. [Kennedy, D.M., Braga, A. A., Piehl, A.M., 1998. The (un)known universe: mapping gangs and gang violence in Boston. Crime Prevention Studies 8, 219–262].     

On the core of characteristic function games associated with exchange networks

An exchange network is a social system in which the actors gain valued resources from bilateral transactions, but an opportunity to negotiate a deal is given only to those pairs of actors whose positions are tied with each other in a fixed communication network. A transaction consists in a mutually agreed-on division of a resource pool assigned to a network line. An additional constraint imposed on such a network restricts the range of transaction sets which may happen in a single negotiation round to those consistent with a given “exchange regime.” Under the one-exchange regime every actor is permitted to make no more than one deal per round. Bienenstock and Bonacich [Bienenstock, E.J., Bonacich, P., 1992. The core as a solution to exclusionary networks. Social Networks 14, 231–243] proposed to represent a one-exchange network with an n-person game in characteristic function form. The aim of this paper is to develop a mathematical theory of games associated with homogenous one-exchange networks (network homogeneity means that all lines are assigned resource pools of the same size). The focus is on the core, the type of solution considered most important in game theory. In particular, all earlier results obtained by Bonacich are re-examined and there is given a new graph-theoretic necessary and sufficient condition for the existence of nonempty core for the game representing a homogenous one-exchange network.     

Centrality in affiliation networks

This paper discusses the conceptualization, measurement, and interpretation of centrality in affiliation networks. Although centrality is a well-studied topic in social network analysis, and is one of the most widely used properties for studying affiliation networks, virtually all discussions of centrality and centralization have concerned themselves with one-mode networks. Bonacich's work on simultaneous group and individual centralities is a notable exception (Social Networks, 1991, 13, 155–168). I begin by outlining the distinctive features of affiliation networks and describe four motivations for centrality indices in affiliation networks. I then consider properties of some existing centrality indices for affiliation networks, including the relationship between centralities for actors and events in these networks, and present a new conceptualization of centrality that builds on the formal properties of affiliation networks and captures important theoretical insights about the positions of actors and events in these networks. These centralities are then illustrated on Galaskiewicz's data on club and board memberships of a sample of corporate executive officers (Social Organization of an Urban Grants Economy. New York: Academic Press, 1985). The conclusion to this paper discusses strengths and weaknesses of centrality indices when applied to affiliation networks.     

Strategic risk communication: Adding value to society

The purpose of this paper is to provide a concise summary of the evolvement and the current state of risk communication research and draw insights from a decade of risk communication studies [Heath, R. L., & Abel, D. D. (1996). Proactive response to citizen risk concerns: Increasing citizens’ knowledge of emergency response practices. Journal of Public Relations Research, 8(3), 151–171; Heath, R. L., & Palenchar, M. (2000). Community relations and risk communication: A longitudinal study of the impact of emergency response messages. Journal of Public Relations Research, 12(2), 131–162; Palenchar, M. J., & Heath, R. L. (2002). Another part of the risk communication model: Analysis of communication processes and message content. Journal of Public Relations Research, 14(2), 127–158; Palenchar, M. J., & Heath, R. L. (2003a). Protracted strategic risk communication: A longitudinal analysis of community's zones of meaning. Paper presented at the conference of the Association for Education in Journalism and Mass Communication, Kansas City, MO; Palenchar, M. J., & Heath, R. L. (2003b). Strategic risk communication: A longitudinal analysis of a community's emergency response awareness and practices. Paper presented at the conference of the National Communication Association, Miami, FL; Palenchar, M. J., & Heath, R. L. (2006). Strategic risk communication campaigns: Some insights from the culmination of a decade of research. Paper presented at the conference of the International Communication Association, Dresden, Germany; Palenchar, M. J., Heath, R. L., & Dunn, E. (2005). Terrorism and industrial chemical production: A new era of risk communication. Communication Research Reports, 22(1), 59–67]. A meta-analysis of the authors’ research based on qualitative and quantitative research methodologies, including professionally conducted telephone interviews, focus groups, in-depth interviews and ethnography, suggests that strategic risk communication based on the concept that ideas and meaning count, transparency, building trust through community outreach and collaborative decision making, acknowledging uncertainty, and narrative enactment are fundamental communication guidelines for good organizations communicating well; keys for risk communication if it is to add value to society.     

The effect of density on the level of bias in the network autocorrelation model

Researchers interested in the effects of social network ties on behavior are increasingly turning to the network autocorrelation model, which allows for the simultaneous computation of individual-level and network-level effects. Earlier research, however, had pointed to the possibility that the maximum likelihood estimates used to compute the network autocorrelation model yielded negatively biased parameter estimates. In this paper we use simulations to examine whether – and the conditions under which – a negative bias exists. We show that the network parameter estimate ρ is negatively biased under nearly all conditions, and that this bias becomes more severe at higher levels of both ρ and network density. We conclude by discussing the implications of these findings for researchers planning to use the network autocorrelation model.     

Equicentrality and network centralization: A micro–macro linkage

This paper investigates a linkage between micro- and macrostructures as an intrinsic property of social networks. In particular, it examines the linkage between equicentrality [Kang, S.M., 2007. A note on measures of similarity based on centrality. Social Networks 29, 137–142] as a conceptualization of a microstructural process (i.e., the likelihood of social actors to be connected with similarly central others) and network centralization as a macrostructural construct, and shows that they have a negative linear association. In other words, when actors are connected with similarly central alters (i.e., high equicentrality), the overall network centralization is low. Conversely, when highly central actors are connected with low-centrality actors (i.e., low equicentrality), the overall network centralization is high. The relationship between degree equicentrality and degree centralization is more significant in observed networks, especially those evolving over time, as compared to random networks. An application of this property is given by venture capital co-investment networks.     

Categorical attribute based centrality: E–I and G–F centrality

In a paper examining informal networks and organizational crisis, Krackhardt and Stern (1988) proposed a measure assessing the extent to which relations in a network were internal to a group as opposed to external. They called their measure the E–I index. The measure is now in wide use and is implemented in standard network packages such as UCINET ( Borgatti et al., 2002). The measure is based on a partition-based degree centrality measure and as such can be extended to other centrality measures and group level data. We explore extensions to closeness, betweenness and eigenvector centrality, and show how to apply the technique to sets of subgroups that do not form a partition. In addition, the extension to betweenness suggests a linkage to the Gould and Fernandez brokerage measures, which we explore.     

Social Capital and economic opportunities

Moving on from [Coleman, J.S., 1990. Foundations of Social Theory. Belknap Press of Harvard University Press, Cambridge, MA, London] and [Putnam, R.D., Leonardi, R., Nanetti, R.Y., 1993. Making Democracy Work Civic Traditions in Modern Italy. Princeton University Press, Princeton, NJ, Chichester], an ever-growing literature claims that repeating trustful interactions in the economy do sediment in higher levels of generalized trust. This aggregate stock of trust is then named Social Capital and treated as an input in the aggregate production function, such as labour, physical capital, or human capital. In this paper we argue that in many instances there is no need for meta-concepts like Social Capital, as trust is often simply the outcome of profit maximization. Whilst approaches that refer to Social Capital ignore the set of economic opportunities, incentives and conflicts behind trust, in this article we propose a simple model to show that when these are taken into account, the roles of trust and Social Capital can be better defined and understood.     

Computing core/periphery structures and permutation tests for social relations data

The core/periphery structure is ubiquitous in network studies. The discrete version of the concept is that individuals in a group belong to either the core, which has a high density of ties, or to the periphery, which has a low density of ties. The density of ties between the core and the periphery may be either high or low. If the core/periphery structure is given a priori, then there is no problem in finding a suitable statistical test. Often, however, the structure is not given, which presents us with two problems, searching for the optimal core/periphery structure, and devising a valid statistical test to replace the one invalidated by the search. UCINET [Borgatti, S.P., Everett, M.G., Freeman, L.C., 2002. UCINET for Windows, Version 6.59: Software for Social Network Analysis. Analytic Technologies, Harvard], the oldest and most trusted network program, gives incorrect answers in some simple cases for the first problem and does not address the second. This paper solves both problems with an adaptation of the Kernighan–Lin search algorithm, and with a permutation test incorporating this algorithm.     

Generalized blockmodeling of valued networks

The paper presents several approaches to generalized blockmodeling of valued networks, where values of the ties are assumed to be measured on at least interval scale. The first approach is a straightforward generalization of the generalized blockmodeling of binary networks [Doreian, P., Batagelj, V., Ferligoj, A., 2005. Generalized Blockmodeling. Cambridge University Press, New York.] to valued blockmodeling. The second approach is homogeneity blockmodeling. The basic idea of homogeneity blockmodeling is that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values. New ideal blocks appropriate for blockmodeling of valued networks are presented together with definitions of their block inconsistencies.     

Rurality discourses and the role of the social enterprise in regenerating rural Scotland

Social enterprises are businesses with primarily social objectives that reinvest their surplus in the community rather than seeking to maximise profit for shareholders. However, there is a debate regarding the drivers and the role of the social enterprise, the outcome of which is expected to have serious implications for the future of the institution [Brady, C., 2003. Social Enterprise development and the Role of the Social Economy in Scotland. CBS Network, Edinburgh]. A ‘reformist’ view supports the position that social enterprises are simple extensions of existing economic systems, whereas a ‘radical’ stance sees them as the embodiment of an alternative vision of running local economies. Development Trusts (DTs) are social enterprises that focus on community regeneration. Our research explored DT stakeholder views regarding the role of DTs in regenerating rural Scotland. Using Q methodology [Barry, J., Proops, J., 1999. Seeking sustainability discourses with Q methodology. Ecological Economics, 28, 337–345], we drew on ‘rurality’ discourses [Frouws, J., 1998. The contested redefinition of the countryside. An analysis of rural discourses in The Netherlands. Sociologia Ruralis 38(1), 54–68] expressed by DT stakeholders in order to investigate how these discourses informed their views. Radical positions were mostly associated with a hedonist rurality discourse and were split into three sub-discourses, whereas reformist positions mostly reflected a utilitarian rurality discourse. There was consensus between discourses in rejecting a primary DT contribution to rural regeneration by substituting state and local authority functions in rural Scotland. Results suggest that stakeholders prefer that DTs develop their own agendas and activity rather than try to substitute unsuccessful state or local authority provision of rural services. Social enterprise strategies and support policies promoting a service-providing role for DTs in rural Scotland should consider this issue if they are to avoid stakeholder objection and contribute to the success of DTs in becoming active vehicles of rural regeneration.     

The use of sparsest cuts to reveal the hierarchical community structure of social networks

We show that good community structures can be obtained by partitioning a social network in a succession of divisive sparsest cuts. A network flow algorithm based on fundamental principles of graph theory is introduced to identify the sparsest cuts and an underlying hierarchical community structure of the network via maximum concurrent flow. Matula [Matula, David W., 1985. Concurrent flow and concurrent connectivity in graphs. In: Alavi, Y., et al. (Eds.), Graph Theory and its Applications to Algorithms and Computer Science. Wiley, New York, NY, pp. 543–559.] established the maximum concurrent flow problem (MCFP), and papers on divisive vs. agglomerative average-linkage hierarchical clustering [e.g., Matula, David W., 1983. Cluster validity by concurrent chaining. In: Felsenstein, J. (Ed.), Numerical Taxonomy: Proc. of the NATO Adv. Study Inst., vol. 1. Springer-Verlag, New York, pp. 156–166 (Proceedings of NATO ASI Series G); Matula, David W., 1986. Divisive vs. agglomerative average linkage hierarchical clustering. In: Gaul, W., and Schader, M. (Eds.), Classification as a Tool of Research. Elsevier, North-Holland, Amsterdam, pp. 289–301; Thompson, Byron J., 1985. A flow rerouting algorithm for the maximum concurrent flow problem with variable capacities and demands, and its application to cluster analysis. Master Thesis. School of Engineering and Applied Science, Southern Methodist University] provide the basis for partitioning a social network by way of sparsest cuts and/or maximum concurrent flow.     

Statistical power of the social network autocorrelation model

The network autocorrelation model has become an increasingly popular tool for conducting social network analysis. More and more researchers, however, have documented evidence of a systematic negative bias in the estimation of the network effect (ρ). In this paper, we take a different approach to the problem by investigating conditions under which, despite the underestimation bias, a network effect can still be detected by the network autocorrelation model. Using simulations, we find that moderately-sized network effects (e.g., ρ = .3) are still often detectable in modest-sized networks (i.e., 40 or more nodes). Analyses reveal that statistical power is primarily a nonlinear function of network effect size (ρ) and network size (N), although both of these factors can interact with network density and network structure to impair power under certain rare conditions. We conclude by discussing implications of these findings and guidelines for users of the autocorrelation model.     

Producing Postman Pat: The popular cultural construction of idyllic rurality

This paper concerns the popular cultural representation of English rurality. It focuses upon Postman Pat, a popular cultural phenomenon which has come to be routinely cited as exemplary and iconic of contemporary imaginings of the English countryside as idyllic. The idea that Anglocentric popular culture (re)produces this sort of ‘rural idyll’ – and that these idylls are particularly laden with cultural and ideological baggage – has been well rehearsed. However, this paper considers a question which has too often been overlooked or taken for granted: how, exactly – and I mean literally, actually, in detail, in practice – does this sort of idyllic rurality come to be constructed? Through conversations with two key figures in the creation of Postman Pat, the paper begins to develop an understanding of some of the everyday, banal, nitty gritty practices, decisions and encounters which must be understood as fundamentally part of the production of (this) ‘rural idyll’.     

Postman Pat and me: Everyday encounters with an icon of idyllic rurality

It is, by now, well accepted that those of us who live with/in contemporary Anglocentric popular culture are presented, from birth, with manifold icons and imaginings of the English countryside as idyllic. Indeed, the idea that, through such popular representations, we encounter and ‘consume’ this sense of ‘rural idyll’ – and a particular, underlying, ideologically laden set of idea(l)s – has been well rehearsed. However, this paper reflects upon a question which has hitherto been often overlooked: what is the (practical, tangible) nature of this ‘consumption’? Approaching this question, the paper re-presents a succession of encounters with one icon of idyllic rurality: Postman Pat. In so doing, the paper develops an understanding of some complex – and frequently banal, odd, happenstance, taken-for-granted – happenings and practices which are fundamentally part of the ‘consumption’ of ‘rural idyll’.     

Network centralization with the Gil Schmidt power centrality index

Network centralization is a network index that measures the degree of dispersion of all node centrality scores in a network from the maximum centrality score obtained in the network. The Gil Schmidt power centrality index was developed for use in describing the political networks of Mexico, Gil and Schmidt [Gil, J., Schmidt, S., 1996a. The origin of the Mexican network of power. In: International Social Network Conference, Charleston, SC, USA, pp. 22–25; Gil, J., Schmidt, S., 1996b. The political network in Mexico. Social Networks 18, 355–381]. Upper bounds for network centralization, using the Gil Schmidt power centrality index, are derived for networks of fixed order and for when the network is bipartite, such as can arise from two mode data. In each case the networks that have maximum network centralization are described.     

Book Reviews

Book reviewed in this article: Agroecology in Action: Extending Alternative Agriculture through Social Networks, by Keith Douglas Warner Country Boys: Masculinity and Rural Life, by Hugh Campbell, Michael Mayerfield Bell, and Margaret Finney Brewing Justice: Fair Trade Coffee, Sustainability, and Survival, by Daniel Jaffee Service Delivery to Rural Older Adults: Research, Policy, and Practice, by R. Turner Goins and John A. Krout Movimientos Sociales de los Trabajadores Agrícolas Asalariados en el noroeste de México, 1970–1995, by Florencio Posadas Segura