title: Incorporating variability into an approximation formula for bond percolation thresholds of planar periodic lattices.
abstract: Approximation formulas to predict values for bond percolation thresholds of periodic graphs make use of certain features of lattice graphs such as dimension and average degree. We show that a relationship exists between the average and second-moment of the degree of a graph and the average degree of its line graph. Using this relationship together with the well-known bond-to-site transformation between the bond percolation model on a graph and the site percolation model on its line graph, we create a new approximation formula that improves the accuracy of bond percolation threshold predictions.
authors.affiliation: Department of Applied Mathematics and Statistics, 302 Whitehead Hall, Johns Hopkins University, Baltimore, Maryland 21218, USA.
authors.forename: John C
authors.initials: JC
authors.lastname: Wierman
authors.forename: Dora Passen
authors.initials: DP
authors.lastname: Naor
authors.forename: Jonathan
authors.initials: J
authors.lastname: Smalletz