Combinatorics Seminar
Bhaskar DasGupta
UIC
Topological implications of negative curvature for biological and social networks
Abstract: In real network applications, one frequently encounters phenomena of the following type:
a. In biological networks, network motifs are often nested.
b. In biological regulatory networks, paths mediating up- or down-regulation of a target node starting from the same
regulator node often have many small crosstalk paths.
c. An eavesdropper with limited sensor ranges can often intercept communications between nodes very far apart from it.
d. In traffic networks, congestion can happen in a node that is not a hub.
Although each of these phenomena can be studied on its own, it is desirable to have a network measure reflecting
salient properties of complex large-scale networks that can explain all these phenomena at one shot. In this talk we
adapt a combinatorial measure of negative curvature (also called hyperbolicity) to parameterized finite networks, and
show that a variety of biological and social networks are hyperbolic. The hyperbolicity property has strong
implications on the higher-order connectivity and other topological properties of these networks. Specifically, we
derive and prove bounds on the distance among shortest or approximately shortest paths in hyperbolic networks, and
explain how implications of these bounds may provide answers to observations such as in a-d above.
A significant part of this talk is based on a joint paper with R. Albert and N. Mobasheri (Physical review E, 89 (3),
032811, 2014). No prior knowledge of metric topology, biology or social science will be assumed.
Monday October 13, 2014 at 3:00 PM in SEO 427