@NetworkFact

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

johndcook.com/blog/complex-networks/
Joined July 2013
  • Tweets4.3K
  • Following19
  • Followers46.3K
223Media
Complex networks johndcook.com/blog/complex-n…
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Gallery of named graphs altermundus.fr/downloads/doc… // 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 johndcook.com/blog/2022/09/0…

Shortest tours of Eurasia and Oceania

Solving the Traveling Salesman Problem for the countries of Europe, Asia, and Oceania.

johndcook.com
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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 graphviz.org/

Graphviz

Please join the Graphviz forum to ask questions and discuss Graphviz. What is Graphviz? Graphviz is open source graph visualization software. Graph visualization is a way of representing structural...

graphviz.org
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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 johndcook.com/blog/2016/01/2…

Bounding graph diameter by its spectrum | network science

Bounding the diameter of a graph by the eigenvalues of associated matrices

johndcook.com
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GraphML file format graphml.graphdrawing.org/
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Topological sort johndcook.com/blog/2023/03/2…

Topological sort

Topological sort with the command line utility tsort. Illustrated with diagram of special function relations.

johndcook.com
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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 github.com/randomjohn/projec… by @randomjohn

project/out/Communities within the statistics blog network.pdf at master · randomjohn/project

SNA project. Contribute to randomjohn/project development by creating an account on GitHub.

github.com
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Adjacency networks for geographical maps johndcook.com/blog/2022/09/1…

Adjacency networks

Finding the adjacency graphs for US states and Texas counties using Mathematica

johndcook.com
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DAG stands for directed acyclic graph.
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Kuratowski's theorem: Every non-planar graph contains at least one subgraph that is an expansion of K_5 or UG.
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UG denotes the utility graph, the complete bipartite graph with two groups of three vertices.
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