COLLOQUIUM OF THE COMPUTATIONAL MATERIALS SCIENCE CENTER AND THE DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES – Limited Path Percolation in Complex Networks – Eduardo Lopez
COLLOQUIUM OF THE COMPUTATIONAL MATERIALS SCIENCE CENTER
AND THE DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES
(CSI 898-Sec 001)
Limited Path Percolation in Complex Networks
Eduardo Lopez, Asst. Professor
Department of Computational and Data Sciences
George Mason University
October 17, 2016, 4:30 pm
Exploratory Hall, Room 3301
We propose a new percolation model in which reachability (a generalization of connectivity) between any pair of nodes is defined on the basis of the relative increase in distance between nodes before and after percolation removal or some other path lengthening process. Reachability is well justified for real-world networks where, contrary to microscopic systems, the ability to explore all possible paths of any length between nodes is not achievable. If path lenghtining exceeds an externally imposed fraction tau, which reflects the specifics of the problem, node pairs are no longer reachable. This concept induces a new form of phase transition, which we call Limited Path Percolation (LPP). We find that LPP induces in many cases first-order phase transitions in contrast to percolation, which is second order. Also, LPP predicts that networks are more fragile than what is suggested by conventional percolation models, where effectively tau is considered infinite (any path length increase is acceptable). In networks, we find that Erdös-Rényi graphs and networks with steep power-law distributions of connectivity exhibit a range of critically reachable clusters between the new reachability transition and the conventional percolation transition. Very heavy tailed power law distributions of connectivity are generally robust to the introduction of the reachability concept and behave as in conventional percolation. The models and results above, as well as some implications for areas such as epidemiology, will be discussed.
Refreshments will be served at 4:15 PM.
Find the schedule at http://www.cmasc.gmu.edu/seminars.htm