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.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
December 2007
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Rényi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior.
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