For any α ∈ (0, 1) and any nα ≤ d ≤ n/2, we show that λ(G) ≤ Cα√d with probability at least 1− 1 n , where G is the uniform random undirected d-regular graph on n vertices, λ(G) denotes its second ...
Understanding the network organization of the brain has been a long-standing challenge for neuroscience. In the past decade, developments in graph theory have provided many new methods for ...
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