Local Leaders in Random Networks

Abstract

We consider local leaders in random uncorrelated networks, i.e. nodes whose degree is higher or equal than the degree of all of their neighbors. An analytical expression is found for the probability of 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 $\sim k^{-{\gamma }_c}$ with ${\gamma }_c=3$. Theoretical results are verified by computer simulations and the importance of finite-size effects is discussed.

4 pages, 2 figures

References in corpus (17)

• Emergence of scaling in random networks
• The structure and function of complex networks
• Epidemic spreading in scale-free networks
• Assortative mixing in networks
• Network robustness and fragility: Percolation on random graphs
• Organization of Growing Random Networks
• Generation of uncorrelated random scale-free networks
• Voter Model on Heterogeneous Graphs
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Pattern Detection in Complex Networks: Correlation Profile of the Internet
• The origin of degree correlations in the Internet and other networks
• Log-Networks
• Application of Statistical Physics to Politics
• Disease Spreading in Structured Scale-Free Networks
• Statistics of Lead Changes in Popularity-Driven Systems
• How does degree heterogeneity affect an order-disorder transition?
• Growing network with j-redirection

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