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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In many real-world networks, average distances are on the order of the log of the number of vertices.

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Two nodes x and y in a directed graph are strongly connected if there is a path from x to y and a path from y to x.

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Visualizing correlations with graphs https://t.co/JssaA2YYKZ

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Two nodes x and y in a directed graph are weakly connected if there is a path from x to y or from y to x.

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Gallery of named graphs https://t.co/azqwe6wNqH // 104-page pdf from Alain Matthes

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A connected graph contains an Eulerian path iff there are zero or two nodes of odd degree.

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Shortest tours of Eurasia and Oceania https://t.co/rKJuZXBUin

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A Hamiltonian path visits each vertex in a graph exactly once.

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An Eulerian path traverses each edge in a graph exactly once.

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Some authors say graph theory started with Euler's solution to the Kӧnigsberg bridge problem in 1736.

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The diameter of a connected graph is the length of the longest geodesic path in the graph.

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Graphviz - Graph Visualization Software https://t.co/1tTLbxwIcN

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If A is the adjacency matrix of a graph, the number of walks from i to j of length r is the ij-th entry of A^r.

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The density of a graph is the ratio of the actual number of edges to the maximum possible number of edges.

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The degree of a vertex is the number of edges connected to it.

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Bounding a graph's diameter by its spectrum https://t.co/avYdk3Agfh

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GraphML file format https://t.co/HCBi0P694B

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Topological sort https://t.co/V7H2AT66I0

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The number of spanning trees in a connected network w/ n nodes equals the product of the nonzero eigenvalues of its Laplacian, divided by n.

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Communities within the statistics blog network https://t.co/GP4LwKIpfa by @randomjohn