TY - JOUR
T1 - Local leaders in random networks
AU - Blondel, V.D.
AU - Hendrickx, J.M.
AU - De Kerchove, C.
AU - Lambiotte, R.
AU - Guillaume, J.-L.
N1 - Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/3/13
Y1 - 2008/3/13
N2 - We consider local leaders in random uncorrelated networks, i.e., nodes whose degree is higher than or equal to the degree of all their neighbors. An analytical expression is found for the probability for a node of degree k to be a local leader. This quantity is shown to exhibit a transition from a situation where high-degree nodes are local leaders to a situation where they are not, when the tail of the degree distribution behaves like the power law ∼ k- γc with γc =3. Theoretical results are verified by computer simulations, and the importance of finite-size effects is discussed.
AB - We consider local leaders in random uncorrelated networks, i.e., nodes whose degree is higher than or equal to the degree of all their neighbors. An analytical expression is found for the probability for a node of degree k to be a local leader. This quantity is shown to exhibit a transition from a situation where high-degree nodes are local leaders to a situation where they are not, when the tail of the degree distribution behaves like the power law ∼ k- γc with γc =3. Theoretical results are verified by computer simulations, and the importance of finite-size effects is discussed.
UR - http://www.scopus.com/inward/record.url?scp=40949096847&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.77.036114
DO - 10.1103/PhysRevE.77.036114
M3 - Article
AN - SCOPUS:40949096847
SN - 1539-3755
VL - 77
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
ER -