TY - JOUR

T1 - Shortest paths and load scaling in scale-free trees

AU - Szabó, Gábor

AU - Alava, Mikko

AU - Kertész, János

PY - 2002/8/7

Y1 - 2002/8/7

N2 - The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the [formula presented] case of the Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.

AB - The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the [formula presented] case of the Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.

UR - http://www.scopus.com/inward/record.url?scp=41349112268&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.66.026101

DO - 10.1103/PhysRevE.66.026101

M3 - Article

AN - SCOPUS:41349112268

SN - 1063-651X

VL - 66

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 - 2

ER -