Friday,
February 16, 2018, 3pm
Location: Planetary Hall Room 212
Eduardo
López
Department
of Computational and Data Sciences
George
Mason University
Limited Path Percolation
Abstract
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 lengthening 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 called 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). However, very heavy-tailed power law
distributions of
connectivity are generally robust to the introduction of the
reachability
concept and behave
as in conventional percolation.