The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

White, Dougľas R.; Harary, Frank

doi:10.1111/0081-1750.00098

Cited by 238 publications

(174 citation statements)

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“…Unable to reconcile their differences, the members of the club split into two factions, with one faction departing to start a separate club. It has been claimed repeatedly that by examining the pattern of friendships depicted in the network (which was compiled before the split happened) one can predict the membership of the two factions 14,20,26,27,[38][39][40] . Figure 3 shows the output of the hierarchical clustering procedure in the form of a tree or 'dendrogram' representing the order in which nodes are grouped together into communities.…”

Section: Hierarchical Clusteringmentioning

confidence: 99%

Communities, modules and large-scale structure in networks

2011

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Networks, also called graphs by mathematicians, provide a useful abstraction of the structure of many complex systems, ranging from social systems and computer networks to biological networks and the state spaces of physical systems. In the past decade there have been significant advances in experiments to determine the topological structure of networked systems, but there remain substantial challenges in extracting scientific understanding from the large quantities of data produced by the experiments. A variety of basic measures and metrics are available that can tell us about small-scale structure in networks, such as correlations, connections and recurrent patterns, but it is considerably more difficult to quantify structure on medium and large scales, to understand the 'big picture'. Important progress has been made, however, within the past few years, a selection of which is reviewed here.A network is, in its simplest form, a collection of dots joined together in pairs by lines (Fig. 1). In the jargon of the field, a dot is called a 'node' or 'vertex' (plural 'vertices') and a line is called an 'edge'. Networks are used in many branches of science as a way to represent the patterns of connections between the components of complex systems [1][2][3][4][5][6] . Examples include the Internet 7,8 , in which the nodes are computers and the edges are data connections such as optical-fibre cables, food webs in biology 9,10 , in which the nodes are species in an ecosystem and the edges represent predator-prey interactions, and social networks 11,12 , in which the nodes are people and the edges represent any of a variety of different types of social interaction including friendship, collaboration, business relationships or others.In the past decade there has been a surge of interest in both empirical studies of networks 13 and development of mathematical and computational tools for extracting insight from network data 1-6 . One common approach to the study of networks is to focus on the properties of individual nodes or small groups of nodes, asking questions such as, 'Which is the most important node in this network?' or 'Which are the strongest connections?' Such approaches, however, tell us little about large-scale network structure. It is this large-scale structure that is the topic of this paper.The best-studied form of large-scale structure in networks is modular or community structure 14,15 . A community, in this context, is a dense subnetwork within a larger network, such as a close-knit group of friends in a social network or a group of interlinked web pages on the World Wide Web (Fig. 1). Although communities are not the only interesting form of large-scale structure-there are others that we will come to-they serve as a good illustration of the nature and scope of present research in this area and will be our primary focus.Communities are of interest for a number of reasons. They have intrinsic interest because they may correspond to functional units within a networked system, an example of the kind of link...

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Section: Hierarchical Clusteringmentioning

confidence: 99%

Communities, modules and large-scale structure in networks

2011

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“…"A group's structural cohesion is equal to the minimum number of actors who, if removed from the group, would disconnect the group" (Moody and White, 2003, p. 109). More formally (White and Harary, 2001), a maximal set S with respect to a property P is one for which every broader set containing S lacks property P, and a k-component is a maximal subgraph of a graph G that is k-connected. When we use the term multiconnectivity we are referring to k-connected graphs, their k-components, and the fact that all nodes in a k-component are k-connected.…”

Section: From Embeddedness To Cohesionmentioning

confidence: 99%

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

White

Owen‐Smith

Moody

et al. 2004

Computational & Mathematical Organization Theory

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Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.

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“…The algorithmic science of finding unique "strong boundaries" of cohesive network sub-groups, as proven mathematically for cohesive blocking (overlap detection for hybrid communities) is barely in its infancy. Yet White and Harary's (2001) time-series predictions of karate club member decisions are replicated in Estrada and Hatano's model, and serve as an example of precisely matching predictive models for how ties dissolve as a club splits in two during a conflict between leaders. For every population in which there are data on the kinds of elements that constitute a culture or subculture, tests can now be constructed using cohesive blocking models and also Estrada's community detection algorithm to predict consensus or other patterns of behavior.…”

Section: The Fallacy That Thought Depends On Languagementioning

confidence: 83%

“…Results are heavily dependent on mathematical theorems about graphs, networks, and relational algebra that capture "necessary connections" (see White 1974;White and Reitz 1983;White and Harary 2001) for results that are not prima facie visible to the observer, as either ethnographer, preceptor of a network graphic, or network participant. Local choices and subsequent behavior in networks, for example, have necessary implications for global features of networks, and vice versa.…”

Section: Deeper Problems: Mind Logics and Worldmentioning

confidence: 99%

“…It was reiterated by Ross (2004:124), who took density as a measure of cohesion, which it is not. White and Harary (2001) were the first to both formulate a formal measure of network cohesion that drew from the theory of graphs, and to test the predictiveness of the concept with a simple empirical example. They predicted how a karate club studied for two years by Zachary (1977) divided its membership between the club owner and the instructor, and the order of secession of members as the teacher formed a new club.…”

Section: The Cohesion and Consensus Hypothesismentioning

confidence: 99%

See 1 more Smart Citation

Social Networks, Cognition, and Culture

White¹

2011

A Companion to Cognitive Anthropology

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NETWORKSNetwork studies are an important adjunct to further development of cognitive anthropology and theory. When reliable means of identifying relational properties of behavior, cognition, and cultural structures or systems are available they help overcome limitations of other types of descriptive studies, descriptive statistics, or ad hoc inferences about how mind, culture, and social behavior interact. RolesRoles form into key network and institutional structures which can be understood in relation to social processes. Network ethnography can also operate in this way to further understanding (White and Johansen 2006:ch. 1). Network studies enhance our understandings of cause and effects of emergent roles and their dynamical patterns of shifting stability, including hierarchy. Finding hierarchy and its network embeddings, for example, often depends on global as well as local information on how local patterns fit within global ones. Both the understanding of global network structure and analysis of micro-macro linkages are additional advantages. If we wanted to find the leaders in a large urban community (see Freeman et al. 1960), for example, we could start from a sample of potential leaders, ask them who the leaders are, and iteratively construct a snowball sample of higher order leaders until finally a leader sub-network or evidence of a single leader emerges. Cohesive groupsCohesive groups have patterned interactions that are self-reinforcing and self-stabilizing in certain spatio-temporal frames. Study of these interactions can also account for individual choices, the emergence of cohesive units as socially and cognitively recognizable

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The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

Abstract: This study shows several ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses

Cited by 238 publications

References 40 publications

Communities, modules and large-scale structure in networks

Communities, modules and large-scale structure in networks

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

Social Networks, Cognition, and Culture

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