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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Given a list of numbers, when can you construct a simple graph whose nodes have those degrees? https://t.co/tjKUX43zzO

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Modularity in a network is a measure of the degree to which nodes associate with like nodes. https://t.co/5ExLfAbtLH

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Graphing Japanese prefectures https://t.co/DSZO97aZ9i

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The eigenvector corresponding to the second smallest eigenvalue of the Laplacian is called the Fiedler vector.

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Hitting time is asymmetric. Commute time c(i, j) = h(i -> j) + h(j -> i) is symmetric.

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The hitting time h(i -> j) is the average number of steps to walk from node i to node j where probability is proportional to edge weight.

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Why are planar graphs so exceptional? https://t.co/XmebT6QAVI

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The reciprocity of a graph is the proportion of edges that are reciprocated.

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In a directed graph, an edge from i to j is reciprocated if there is also an edge from j to i.

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The betweenness centrality of a point is the number of geodesic paths that pass through the point.

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The Petersen graph serves as a counterexample to many would-be graph conjectures. https://t.co/4fTlUnZnPl

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Basic theory of expander graphs by Terence Tao https://t.co/MG2nBw2eR5

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A knight's random walk on a graph https://t.co/HUna7voreg

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A regular graph is one in which all nodes have the same degree.

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Laboratory for Web Algorithmics https://t.co/1alDAsLdFt

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Applied algebraic topology and sensor networks https://t.co/52o1xG5dse [24 MB pdf]

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Katz centrality https://t.co/Cf9H0OKFx8

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Python software for compressed sparse graphs: https://t.co/89cVtShTcm

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The original 'six degrees of separation' paper: 'An experimental study of the small world problem' https://t.co/qlys0fqbnw [pdf]

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Mickey Mouse Sphere Theorem https://t.co/sip3y5arsC