Phys. Rev. E 77, 036114 (2008) [5 pages]Local leaders in random networksReceived 27 July 2007; published 13 March 2008 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. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.77.036114
DOI:
10.1103/PhysRevE.77.036114
PACS:
89.75.Fb, 89.75.Hc, 87.23.Ge, 05.90.+m
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