Large Network Concepts and Small Network Characteristics
Wednesday, November 19, 2003 - 1:30pm - 2:20pm
Richard Rothenberg (Emory University)
The characteristics of large networks—degree distribution, small world phenomena, community structure, assortatitivity, clustering, vulnerability to attack, etc.—may not be fully recognizable in the smaller (by 5-7 orders of magnitude) networks within which disease transmission takes place. The smoothing afforded by size may not protect small network from unpredictable manifestations that result from underlying heterogeneity and attendant sampling variability. To explore the characteristics of small networks, we have assembled 15 data sets from completed network studies that focused on the transmission of STDs and HIV. These studies reveal underlying heterogeneity in their demographic characteristics, risk behaviors, and disease prevalence, but some similarities with regard to degree distribution, clustering and, depending on the predominant risks, assortatitivity. For example, the aggregated degree distribution (a composite totaling >14,000 dyads) is scale-free (that is, the Cumulative Probability Distribution is linear in the log-log scale, thus fitting a power law curve with an coefficient of ~2.0), as are most of the degree distribution for individual studies (albeit with considerably more “noise”). Clustering greater than that predicted for random graphs is present in all the network studies that permitted examination of components. Short mean path lengths between persons within components, a manifestation of the small world effect, are universally present. Such observations provide substantiation that small networks may behave similarly to large ones, despite greater variability and sampling uncertainties and provide some empirical validation of the theoretical basis for an apparent lack of epidemic threshhold and continued low level endemic disease transmission of some STDs and HIV in these microsettings.