TY - JOUR

T1 - Percolation of spatially constraint networks

AU - Li, Daqing

AU - Li, Guanliang

AU - Kosmidis, Kosmas

AU - Stanley, H. E.

AU - Bunde, Armin

AU - Havlin, Shlomo

PY - 2011/3

Y1 - 2011/3

N2 - We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)∼r -δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2<δ<4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ<2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ>4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ<1, the percolation transition is mean field. For 1<δ<2, the critical exponents depend on δ, while for δ>2 there is no percolation transition as in regular linear chains.

AB - We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)∼r -δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2<δ<4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ<2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ>4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ<1, the percolation transition is mean field. For 1<δ<2, the critical exponents depend on δ, while for δ>2 there is no percolation transition as in regular linear chains.

UR - http://www.scopus.com/inward/record.url?scp=79953658627&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/93/68004

DO - 10.1209/0295-5075/93/68004

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AN - SCOPUS:79953658627

SN - 0295-5075

VL - 93

JO - EPL

JF - EPL

IS - 6

M1 - 68004

ER -