Network Fact

Complex networks johndcook.com/blog/complex-n…

A scale-free network is one in which the distribution of node degrees follows a power law distribution.

The tendency for people to associate with people unlike themselves is called disassortative mixing.

The tendency for people to associate with people like themselves is called homophily or assortative mixing.

A k-plex is a generalization of a clique. Every vertex in a k-plex of size n is connected to at least n-k vertices in the k-plex.

Open problems in graph theory openproblemgarden.org/category/graph…

A clique in an undirected graph is a maximal subset mutually connected vertices.

Critical path method for project management en.wikipedia.org/wiki/Critical_…

Dijkstra's algorithm finds the shortest paths from a node s to all other nodes in a graph with non-negative edge weights. Run time O(V²).

Notes on eigenvalues of graphs by László Lovász web.cs.elte.hu/~lovasz/eigenv… [pdf]

Poincare-Hopf for Vector Fields on Graphs quantumcalculus.org/poincare-hopf-…

Eigenvector centrality for graphs johndcook.com/blog/2024/06/0…

Prim's algorithm for finding minimum spanning trees requires O(E + V log V) time.

An articulation point is a vertex whose removal disconnects a graph. A bridge is an edge whose removal disconnects a graph.

Eigenvalues of random power law graphs math.ucsd.edu/~fan/wp/eigen.…

Roughly speaking, category theory is graph theory with additional structure to represent composition.

λ_2 is called the algebraic connectivity of a graph, sometimes also called the spectral gap.

If λ_2, the second eigenvalue of the graph Laplacian, is positive the graph is connected.

Network analysis of Game of Thrones qz.com/650796

Expected time for a random walk to visit every node in a graph johndcook.com/blog/2017/01/0…

The eigenvalues of the graph Laplacian are denoted λ_1, λ_2, ... in non-decreasing order, not necessarily distinct.