TY - JOUR
T1 - Analytical results for bond percolation and k -core sizes on clustered networks
AU - Gleeson, James P.
AU - Melnik, Sergey
PY - 2009/10/26
Y1 - 2009/10/26
N2 - An analytical approach to calculating bond percolation thresholds, sizes of k -cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated using a generalization of Trapman's model of cliques embedded in treelike random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a nonzero percolation (epidemic) threshold.
AB - An analytical approach to calculating bond percolation thresholds, sizes of k -cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated using a generalization of Trapman's model of cliques embedded in treelike random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a nonzero percolation (epidemic) threshold.
UR - http://www.scopus.com/inward/record.url?scp=70449411707&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.80.046121
DO - 10.1103/PhysRevE.80.046121
M3 - Article
AN - SCOPUS:70449411707
SN - 1539-3755
VL - 80
SP - -
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 4
M1 - 046121
ER -