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Bilal Khan, Department of Sociology, UNL New directions in inference on social networks

Date: Time: 4:00 pm–4:50 pm
Avery Hall
Additional Info: AVH
Contact: David Pitts, dpitts2@unl.edu
For social scientists studying subpopulations whose members experience disproportionate health issues, size estimates are important information as they are necessary for creating effective public policy. At the same time, the problem of size estimation is exceedingly difficult when the subpopulations of interest are hard to reach, as is the case when social stigma is associated with group membership or when group members require anonymity because of their involvement in illegal activities.
The resolution of such difficulties is among the concerns of social network analysis, which is one of the many applications of graph theory. In this talk, I will present a recent result in social network analysis relating to the properties of random graphs. Informally stated, the question considered is: Can one estimate the size of a graph merely from the combinatorics and geometry of a small induced subgraph? I will show that, suitably formalized, the question can be answered positively for a large class of random graphs.
In the second half of the talk, I will present some open problems in social network analysis, including some results in disease epidemiology which have been verified experimentally, but have yet to be proven formally. I will also describe new social data collection paradigms based on emerging mHealth technologies being developed at the University of Nebraska-Lincoln, and the implications of these advances on the quantification of social networks. This new and imminent data suggest a need for extensions to classical graph-theoretic formalisms, in anticipation of concomitant advances in our understanding of mathematical properties of the Human Sociome.

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