The number of distinct eigenvalues of a graph.

The number of distinct Laplacian eigenvalues of a graph.

The number of distinct eigenvalues of the distance Laplacian of a connected graph.

The detour number of a graph. This is the number of vertices in a longest induced path in a graph. Note that [1] defines the detour number as the number of edges in a longest induced path, which is unsuitable for the empty graph.

The 2-dynamic chromatic number of a graph. A $k$-dynamic coloring of a graph $G$ is a proper coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-dynamic chromatic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring. This statistic records the $2$-dynamic chromatic number of a graph.

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

The length of a shortest maximal path in a graph.

The length of a longest path in a graph.

The rank of the adjacency matrix of a graph.

The minimum rank of a graph. The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices whose entry in row $i$ and column $j$ (for $i\neq j$) is nonzero whenever $\{i, j\}$ is an edge in $G$, and zero otherwise.