Breadth-first search runs in time linear in the size of the adjacenty-list representation of a graph.

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

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.

Visualizing correlations with graphs johndcook.com/blog/2022/09/2…

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.

Gallery of named graphs altermundus.fr/downloads/doc… // 104-page pdf from Alain Matthes

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

Shortest tours of Eurasia and Oceania johndcook.com/blog/2022/09/0…

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

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

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

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

Graphviz - Graph Visualization Software graphviz.org/

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.

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

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

Bounding a graph's diameter by its spectrum johndcook.com/blog/2016/01/2…

GraphML file format graphml.graphdrawing.org/

Topological sort johndcook.com/blog/2023/03/2…

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.