TY - JOUR
T1 - Cumulated social roles
T2 - The duality of persons and their algebras
AU - Breiger, Ronald L.
AU - Pattison, Philippa E.
N1 - Funding Information:
* We are grateful to John F. Padgett for sharing with us his extensive data set on social networks in Fifteenth-Century Florence, and for his willingness to attempt to educate us on all the relevant particulars. Lawrence L. Wu provided useful comments on our entire approach and kept us on the right track on several occasions. Discussions with several individuals helped us to clarify our thoughts about the issues treated in this paper: Phipps Arable, John Boyd, David M. Krackhardt, Michael J. Mandel, John W. Meyer, John F. Padgett, Douglas R. White., Harrison C. White, and Christopher Winship. We are grateful for the support of the University of Melbourne, particularly of the Department of Psychology, and of the Center for Advanced Study in the Behavioral Sciences, including a Fellowship (1985-86) to Breiger and support through National Science Foundation Grant BNS-8011494. The research reported in this paper resulted from a thoroughly collaborative on-going project; the order of authorship is alphabetical. ** Department of Sociology, Comell University, Ithaca, NY 14853, U.S.A. *** Department of Psychology, University of Melbourne, Parkville, Victoria 3052, Australia.
PY - 1986/9
Y1 - 1986/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0039587127&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0039587127&partnerID=8YFLogxK
U2 - 10.1016/0378-8733(86)90006-7
DO - 10.1016/0378-8733(86)90006-7
M3 - Article
AN - SCOPUS:0039587127
SN - 0378-8733
VL - 8
SP - 215
EP - 256
JO - Social Networks
JF - Social Networks
IS - 3
ER -