Sampling properties of random graphs: The degree distribution
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Sampling properties of random graphs : The degree distribution. / Stumpf, Michael P.H.; Wiuf, Carsten.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 3, 036118, 01.09.2005.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Sampling properties of random graphs
T2 - The degree distribution
AU - Stumpf, Michael P.H.
AU - Wiuf, Carsten
PY - 2005/9/1
Y1 - 2005/9/1
N2 - We discuss two sampling schemes for selecting random subnets from a network, random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distributions of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find that this condition is satisfied by classical random graphs; for the vast majority of networks this condition will, however, not be met. We furthermore discuss the case where the probability of sampling a node depends on the degree of a node and we find that even classical random graphs are no longer closed under this sampling regime. We conclude by relating the results to real Eschericia coli protein interaction network data.
AB - We discuss two sampling schemes for selecting random subnets from a network, random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distributions of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find that this condition is satisfied by classical random graphs; for the vast majority of networks this condition will, however, not be met. We furthermore discuss the case where the probability of sampling a node depends on the degree of a node and we find that even classical random graphs are no longer closed under this sampling regime. We conclude by relating the results to real Eschericia coli protein interaction network data.
UR - http://www.scopus.com/inward/record.url?scp=28844465436&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.72.036118
DO - 10.1103/PhysRevE.72.036118
M3 - Journal article
AN - SCOPUS:28844465436
VL - 72
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 3
M1 - 036118
ER -
ID: 203903561