A simple object (one point in m-dimensional space) is the resultant of the evolving matrix polynomial of walks in the irreducible aperiodic network structure of the first order DeGroot (weighted averaging) state-space process. This paper draws on a second order generalization the DeGroot model that allows complex object resultants, i.e, multiple points with distinct coordinates, in the convex hull of the initial state-space. It is shown that, holding network structure constant, a unique solution exists for the particular initial space that is a sufficient condition for the convergence of the process to a specified complex object. In addition, it is shown that, holding network structure constant, a solution exists for dampening values sufficient for the convergence of the process to a specified complex object. These dampening values, which modify the values of the walks in the network, control the system's outcomes, and any strongly connected typology is a sufficient condition of such control.
Areas of interest include social psychology, social networks, mathematical sociology, and formal organizations. Friedkin’s publications, in the field of structural social psychology, have appeared in the American Sociological Review, American Journal of Sociology, Annual Review of Sociology, Social Psychology Quarterly, Administrative Science Quarterly, Social Forces, and Journal of Mathematical Sociology, among other outlets. His two books are A Structural Theory of Social Influence (Cambridge University Press, 1998), and Social Influence Network Theory (Cambridge University Press, 2011), with Eugene Johnsen. He has served on the editorial boards of ASR, AJS, SPQ, and JMS. In 2005, he was elected to the Sociological Research Association.