The Statistical Analysis of Local Structure in Social Networks

63 Pages Posted: 5 Jan 2007 Last revised: 17 Aug 2010

See all articles by Paul W. Holland

Paul W. Holland

University of California, Berkeley; National Bureau of Economic Research (NBER)

Samuel Leinhardt


Date Written: June 1974


We introduce the concept of a triad census of a digraph arid show how it can be used to enumerate various types of subgraph configurations. We give the basic probabilities needed for computing means and variances for a triad census under the U-MAN distribution for digraphs. These concepts are combined to provide a way of testing propositions about social structure using sociometric data. An application to 408 sociograms is given.

Suggested Citation

Holland, Paul W. and Leinhardt, Samuel, The Statistical Analysis of Local Structure in Social Networks (June 1974). NBER Working Paper No. w0044. Available at SSRN:

Paul W. Holland (Contact Author)

University of California, Berkeley ( email )

Department of Education
Berkeley, CA 94720
United States
510-642-6476 (Phone)
510-642-0709 (Fax)

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

Samuel Leinhardt


4341 Schenley Farms Terrace
PGH, PA 15213
United States

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