Ronald L. Breiger

Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions

Networks of several distinct types of social tie are aggregated by a dual model that partitions a population while simultaneously identifying patterns of relations. Concepts and algorithms are demonstrated in five case studies involving up to 100 persons and up to eight types of tie, over as many as 15 time periods. In each case the model identifies a concrete social structure. Role and position concepts are then identified and interpreted in terms of these new models of concrete social structure. Part II, to be published in the May issue of this Journal (Boorman and White 1976), will show how the operational meaning of role structures in small populations can be generated from the sociometric blockmodels of Part I.

An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

Abstract A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [ −1 1 1 −1 ]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White ( White, Boorman & Breiger, 1976 ). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.

Transformation of social networks in the late pre-Hispanic US Southwest.

The late pre-Hispanic period in the US Southwest (A.D. 1200–1450) was characterized by large-scale demographic changes, including long-distance migration and population aggregation. To reconstruct how these processes reshaped social networks, we compiled a comprehensive artifact database from major sites dating to this interval in the western Southwest. We combine social network analysis with geographic information systems approaches to reconstruct network dynamics over 250 y. We show how social networks were transformed across the region at previously undocumented spatial, temporal, and social scales. Using well-dated decorated ceramics, we track changes in network topology at 50-y intervals to show a dramatic shift in network density and settlement centrality from the northern to the southern Southwest after A.D. 1300. Both obsidian sourcing and ceramic data demonstrate that long-distance network relationships also shifted from north to south after migration. Surprisingly, social distance does not always correlate with spatial distance because of the presence of network relationships spanning long geographic distances. Our research shows how a large network in the southern Southwest grew and then collapsed, whereas networks became more fragmented in the northern Southwest but persisted. The study also illustrates how formal social network analysis may be applied to large-scale databases of material culture to illustrate multigenerational changes in network structure.

Cumulated social roles: The duality of persons and their algebras☆

Abstract The study of social roles from the perspectives of individual actors, and the relation of graph homomorphisms to semigroup homomorphisms, have been the two most prominent topics to emerge from the recent resurgence of progress made on the algebraic analysis of social networks. Through our central construction, the cumulated person hierarchy, we present a framework for elaborating and extending these two lines of research. We focus on each actor in turn as ego, and we articulate what we believe to be the fundamental duality of persons and their algebras. We derive graph and semigroup homomorphisms for three algebras containing 81, 43, and 93 elements, respectively. Throughout, our discussion of theoretical issues is oriented toward an empirical application to the Padgett data set on conspiracy and faction in Renaissance Florence.

Institutional Logics from the Aggregation of Organizational Networks: Operational Procedures for the Analysis of Counted Data

We address some problems of network aggregation that are central to organizational studies. We show that concepts of network equivalence (including generalizations and special cases of structural equivalence) are relevant to the modeling of the aggregation of social categories in cross-classification tables portraying relations within an organizational field (analogous to one-mode networks). We extend our results to model the dual aggregation of social identities and organizational practices (an example of a two-mode network). We present an algorithm to accomplish such dual aggregation. Within the formal and quantitative framework that we present, we emphasize a unified treatment of (a) aggregation on the basis of structural equivalence (invariance of actors within equivalence sets), (b) the study of variation in relations between structurally equivalent sets, and (c) the close connections between aggregation within organizational networks and multi-dimensional modeling of organizational fields.

Lattices and dimensional representations: Matrix decompositions and ordering structures

Abstract This paper is concerned with some methods that attempt to provide simultaneous representation of dual relationships, such as ties of membership that connect persons and groups, or connections between organizations and agendas. We focus on vector space and lattice representations, and on techniques for simplifying the structure of dual networks. We demonstrate some fundamental similarities among these approaches.

Dualities of Culture and Structure: Seeing Through Cultural Holes

Just three decades ago, Peter Blau declared that “social structure is not culture.” Blau averred that the study of the quantitative dimensions of social structure had long been neglected, “two exceptions being Harrison C. White and Bruce H. Mayhew,” and moreover that the quantitative dimensions constitute the core of social structure and “distinguish it from culture” (Blau 1977: 245). Indeed, the oft-proclaimed “breakthrough” in the 1970s that “firmly established” network analysis as a method of structural analysis (Scott 2000: 33-37) defined itself in opposition to culture. White and his coauthors, of whom I was one (White et al. 1976: 734), seemed to take pride in announcing that “the cultural and social-psychological meanings of actual ties are largely bypassed…. We focus instead on interpreting the patterns among types of tie.”

Explorations in structural analysis : dual and multiple networks of social interaction

1. Introduction 2. The Duality of Persons and Groups 3. Career Attributes and Network Structure: A Blockmodel Study of a Biomedical Specialty 4. Toward an Operational Theory of Community Elite Structures

Dimensions of Corporate Social Capital: Toward Models and Measures

Despite an emerging consensus on the importance of corporate social capital, little work has been done on the analytical problem of which aspects, precisely, of a corporate network might be identified as manifesting the concept. Where in a specific configuration of network ties is the corporate social capital located? Is network capital a unitary phenomenon or are there various ways to conceptualize it? In addressing these questions, we formulate models for corporate networks that produce counts for the expected number of ties between each pair of actors on the basis of sets of parameters which are themselves measures of network capital. The model we prefer decomposes a network into separable dimensions comprising status, volume, and proximity. We apply the models to a network of ‘doing deals’ in which billions of dollars of finance capital was raised by syndicates of major U.S. investment banks, data of Eccles and Crane (1988). We show that the model performs well with respect to empirical validity. The modeling framework can be applied and extended to other corporate network settings, and provides measures appropriate for theoretical analyses of markets and corporate relations conceptualized as embedded within social fields.

Ontologies, methodologies, and new uses of Big Data in the social and cultural sciences:

In our Introduction to the Conceiving the Social with Big Data Special Issue of Big Data & Society, we survey the 18 contributions from scholars in the humanities and social sciences, and highlight several questions and themes that emerge within and across them. These emergent issues reflect the challenges, problems, and promises of working with Big Data to access and assess the social. They include puzzles about the locus and nature of human life, the nature of interpretation, the categorical constructions of individual entities and agents, the nature and relevance of contexts and temporalities, and the determinations of causality. As such, the Introduction reflects on the contributions along a series of binaries that capture the dualities and dynamisms of these themes: Life/Data; Mind/Machine; and Induction/Deduction.