Events in MathSys and Complexity Science
This is a calendar page detailing events within the MathSys CDT. It also acts as a booking diary for the Seminar Room D1.07. To book D1.07 please email Sheetal.Sharma@warwick.ac.uk
Please note that your event booking is for D1.07 only. The adjacent common room is a private area for the MathSys Centre that cannot used as part of your booking.
MathSys CDT events have priority for D1.07 room bookings.
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Complexity Forum- Eduardo Lopez
Title: Limited Path Percolation in Complex Networks
Abstract:
We propose a new percolation model in which communication (connectivity) between any pair of nodes is defined on the basis of the relative increase in distance between nodes before and after percolation removal. This definition is well justified for real-world networks where, contrary to microscopic systems, the ability to explore all possible paths between nodes is not achievable. By defining two nodes as connected if their distance after percolation removal does not increase beyond a chosen factor A>1, we can study the size of the largest "communicating cluster" after removal of a fraction of the network links or nodes. Factor A represents a percentage of length increase that is acceptable in order for pairs of nodes to preserve communication. For a large class of networks we find analytically a new "limited path percolation transition" which is a function of the original network structure and A. The usual percolation definition is recovered when A is allowed to be infinite. Above the limited path percolation transition, a "spanning communicating cluster" of linear size with respect to the original network emerges. Between the usual percolation threshold and the new limited path percolation threshold, the largest communicating cluster has power-law size. Our analytical results are supported by simulations on real and model networks. This new model is of great importance in network design, routing algorithms, and immunization strategies, where short paths are most relevant.