### DIMACS Computational and Mathematical Epidemiology Seminar Series

Title: A new clustering coefficient

Speaker: **Sara Soffer**, Rutgers University

Date: October 25, 2004, 11:30 - 12:50

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The clustering coefficient quantifies how well connected are
the neighbors of a vertex in a graph. In real networks it
decreases with the vertex degree, which has been taken as a
signature of the network hierarchical structure. Here we show that
this signature of hierarchical structure is a consequence of
degree correlation biases in the clustering coefficient
definition. We introduce a new definition in which the degree
correlation biases are filtered out, and provide evidence that in
real networks the clustering coefficient is constant or decays
logarithmically with vertex degree.

A joint work with Alexei V\'{a}zquez, Center for Complex
Network Research, University of Notre-Dame.