Network Fact

Daily tweets about networks, graph theory, and related topics from @JohnDCook

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Complex networks

https://t.co/jv4vApLjF9

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Frucht’s theorem: Every finite group is the group of symmetries of a finite undirected graph.

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Graph isomorphism between NBA and MLB https://t.co/bnta4tOXPa

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A tree is a connected, undirected graph with no closed loops.

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Preferential attachment models https://t.co/A9BJXib5bH

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'The founders of Google computed the Perron-Frobenius eigenvector of the web graph and became billionaires.' -- A. Brouwer and W. Haemers

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Rook graphs and Paley graphs https://t.co/4B1muwk1FJ

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The igraph network library comes in C, R, Python, and Ruby versions. https://t.co/kaZJpQCKos

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Heiko Harboth’s conjecture: Every planar graph can be drawn with edges of integer length.

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Coloring the queen's graph https://t.co/fNvZleK9It

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For bibliographic coupling matrix B, b_ij = # of vertices that nodes i and j both point to.

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For cocitation matrix C, c_ij = # of vertices with edges pointing to both nodes i and j.

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If A is the adjacency matrix of a directed graph, C = A A^T is the cocitation matrix and B = A^T A is the bibliographic coupling matrix.

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Bipartite graphs and the signless Laplacian https://t.co/3OCFQpe7iK

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A tree with n vertices has n-1 edges. Conversely, a connected graph with n vertices and n-1 edges must be a tree.

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A graph is acyclic iff all eigenvalues of its adjacency matrix are zero.

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You can tell whether a graph is regular from the spectrum of its adjacency, Laplacian, or signless Laplacian matrix.

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The local clustering coefficient of a node is the proportion of pairs of its neighbors that are connected.

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Graph Complements of Cyclic Graphs https://t.co/l29G7tA6lM

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The recently proven imbalance conjecture

https://t.co/1kQhxGzmSc

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Power-law distributions in empirical data https://t.co/VjWoh7S4Vr