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www.jeremykun.com | ||
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jeremykun.wordpress.com
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| | | | | Define the Ramsey number $ R(k,m)$ to be the minimum number $ n$ of vertices required of the complete graph $ K_n$ so that for any two-coloring (red, blue) of the edges of $ K_n$ one of two things will happen: There is a red $ k$-clique; that is, a complete subgraph of $ k$... | |
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www.nature.com
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| | | | | Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, degree difference (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and s... | |
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blog.demofox.org
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| | | | | The last post showed how random Hamiltonian cycles on a graph (a path that visits each node exactly once) could efficiently handle ranking of a large number of items, by doing sparse pairwise voting (https://blog.demofox.org/2023/09/01/sparse-pairwise-voting-or-tournaments-implementing-some3-voting/). That algorithm needed to generate multiple Hamiltonian cycles which didn't use any graph edges already used by other cycles, and... | |
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www.kahlillechelt.com
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