TOPOLOGY AND DYNAMICS OF COMPLEX SOCIAL NETWORKS

The problem of modeling complex social networks is considered from three per-spectives: The problem of describing network topology; the problem of modeling dynamic processes on networks; and the problem of network sampling. These perspectives are highly complementary, each providing results with applications to one other. With respect to network topology, two main results are presented: An algorithm is presented capable of combining two measures of network struc-ture, the degree distribution and the clustering coe±cient. It is found that just two mechanisms are required to achieve any desired combination of these metrics{ network growth, combined with preferential attachment. Secondly, a mathemat-ical model of one class of complex network, semi-random networks, is presented which is capable of elucidating the structure of semi-random networks in greater detail then had been achieved with previous models. Among other results, this theory allows one to calculate the expected number of neighbors at a given dis-tance from a randomly chosen node, and to compute the mean path length inside the giant component. Network dynamics are investigated with a simple epidemic model, the SIR (Susceptible Infected Removed) model. A mathematical theory is presented for predicting epidemic incidence for SIR dynamics in semi-random networks. Finally, the problem of network sampling is considered. A probability based estimation theory is presented for Respondent Driven Sampling (RDS). The theory enhances RDS by o®ering greater analytical tractability, analytical variance estimation, and the estimation of means of continuous variables. BIOGRAPHICAL SKETC