Samuel Leinhardt

Bio: Samuel Leinhardt is an academic researcher from Carnegie Mellon University. The author has contributed to research in topics: Exploratory data analysis & Social network. The author has an hindex of 20, co-authored 36 publications receiving 6520 citations.

An Exponential Family of Probability Distributions for Directed Graphs

Abstract: Directed graph (or digraph) data arise in many fields, especially in contemporary research on structures of social relationships. We describe an exponential family of distributions that can be used for analyzing such data. A substantive rationale for the general model is presented, and several special cases are discussed along with some possible substantive interpretations. A computational algorithm based on iterative scaling procedures for use in fitting data is described, as are the results of a pilot simulation study. An example using previously reported empirical data is worked out in detail. An extension to multiple relationship data is discussed briefly.

Transitivity in Structural Models of Small Groups

Abstract: Our purpose here is to show how various deterministic models for the structure of interpersonal relations in small groups may all be viewed as special cases of a single model: namely, a transitive graph (t-graph). This exercise serves three purposes. First, the unified approach renders much of the mathematical discussion surrounding these various models quite transparent. Many of the arguments boil down to nothing more than defining certain equivalence relations and looking at the resulting equivalence classes. Second, our focus on the general model may stimulate the search for other useful specializations besides those indicated here. We discuss two ways of specializing the model-restrictions on edges and

A Method for Detecting Structure in Sociometric Data

Abstract: The authors focus on developing standardized measures for models of structure in interpersonal relations. A theorem is presented which yields expectations and variances for measures based on triads. Random models for these measures are discussed and the procedure is carried out for a model of a partial order. This model contains as special cases a number of previously suggested models, including the structural balance model of Cartwright and Harary, Davis's clustering model, and the ranked-clusters model of Davis and Leinhardt. In an illustrative exmaple, eight sociograms are analyzed and the general model is compared with the special case of ranked clusters.

Local Structure in Social Networks

Abstract: This chapter is part of a continuing research series and reports work that is collaborative in every respect. The order of our names on this and our previous reports is alphabetical. National Science Foundation Grants GS-39778 to Carnegie-Mellon University and GJ-1 154X2 to the National Bureau of Economic Research, Inc., provided financial support. We are grateful to James A. Davis, J. Richard Dietrich, and Christopher Winship for aid in conducting this research and to Richard Hill for computer programing. This chapter was written when Paul Holland was with the Computer Research Center for Economics and Management Science of the National Bureau of Economic Research, Inc.

The Strength of Weak Ties

Abstract: Analysis of social networks is suggested as a tool for linking micro and macro levels of sociological theory. The procedure is illustrated by elaboration of the macro implications of one aspect of small-scale interaction: the strength of dyadic ties. It is argued that the degree of overlap of two individuals' friendship networks varies directly with the strength of their tie to one another. The impact of this principle on diffusion of influence and information, mobility opportunity, and community organization is explored. Stress is laid on the cohesive power of weak ties. Most network models deal, implicitly, with strong ties, thus confining their applicability to small, well-defined groups. Emphasis on weak ties lends itself to discussion of relations between groups and to analysis of segments of social structure not easily defined in terms of primary groups.

The Structure and Function of Complex 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.

Community detection in graphs

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.

Network Motifs: Simple Building Blocks of Complex Networks

Abstract: Complex networks are studied across many fields of science. To uncover their structural design principles, we defined “network motifs,” patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks. We found such motifs in networks from biochemistry, neurobiology, ecology, and engineering. The motifs shared by ecological food webs were distinct from the motifs shared by the genetic networks of Escherichia coli and Saccharomyces cerevisiae or from those found in the World Wide Web. Similar motifs were found in networks that perform information processing, even though they describe elements as different as biomolecules within a cell and synaptic connections between neurons in Caenorhabditis elegans. Motifs may thus define universal classes of networks. This