Network Fact @NetworkFact
Daily tweets about networks, graph theory, and related topics from @JohnDCook johndcook.com/blog/complex-n… Joined July 2013-
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UG denotes the utility graph, the complete bipartite graph with two groups of three vertices.
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K_n denotes the complete graph with n vertices, i.e. every vertex connected to every other vertex.
'A Random Walks Perspective on Maximizing Satisfaction and Profit' merl.com/publications/T…
Measuring connectivity with graph Laplacian eigenvalues johndcook.com/blog/2016/01/0…
Four color map theorem: the chromatic number of a planar graph is at most 4.
The largest eigenvalue of the adjacency matrix of a graph is bounded below by sqrt(d_max) and by the average degree of all nodes.
The largest eigenvalue of the adjacency matrix of a graph is <= d_max, the largest degree of any node.
Frucht’s theorem: Every finite group is the group of symmetries of a finite undirected graph.
Graph isomorphism between NBA and MLB johndcook.com/blog/2023/03/0…
A tree is a connected, undirected graph with no closed loops.
Preferential attachment models …ntuallyalmosteverywhere.wordpress.com/2013/08/05/pre…
'The founders of Google computed the Perron-Frobenius eigenvector of the web graph and became billionaires.' -- A. Brouwer and W. Haemers
Rook graphs and Paley graphs johndcook.com/blog/2019/11/1…
The igraph network library comes in C, R, Python, and Ruby versions. igraph.org
Heiko Harboth’s conjecture: Every planar graph can be drawn with edges of integer length.
Coloring the queen's graph johndcook.com/blog/2024/01/3…
For bibliographic coupling matrix B, b_ij = # of vertices that nodes i and j both point to.
For cocitation matrix C, c_ij = # of vertices with edges pointing to both nodes i and j.
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.
Bipartite graphs and the signless Laplacian johndcook.com/blog/2016/01/1…
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