Social Semigroups: A Unified Theory of Scaling and Blockmodelling As Applied to Social Networks

by John P. Boyd

Social Semigroups organizes the algebraic theory of relations and semigroups as it applies to social networks. The algebraic theory is used to analyze and describe social relations. The two problems of scaling Euclidean space and of discrete blockmodeling are unified by the theory of Green relations and solved by means of the singular value of decomposition and simulated annealing, respectively. This fascinating work is the first book to give a self-contained presentation of the areas of semigroup and lattice theory that are necessary for the theory of social relations. It is also the first to apply simulated annealing to the combinatorial problem of finding an optimal fit to a discrete model.

280 pages, Hardcover

First published March 1, 1991

About the author

John P. Boyd joined the faculty at the University of Michigan in 1977 and has been professor of atmospheric, oceanic, and space science in the College of Engineering since 1988. Concurrently, he was the founding associate director of the Laboratory for Scientific Computation (now the Michigan Institute for Computational Discovery and Engineering) and as such created the university's M. S. and Ph.D. degrees in scientific computing. His previous books are Chebyshev and Fourier Spectral Methods, 2nd edition,(Dover, 2001) and Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics (Springer, 1998). He has also published 240 journal articles in atmospheric and oceanic dynamics, nonlinear waves, physics, and Chebyshev, Fourier, and RBF spectral methods, as well as 20 science fiction stories.