The skewness of a graph. For a graph $G$, the '''skewness''' of $G$ is the minimum number of edges of $G$ whose removal results in a planar graph.

The minimal crossing number of a graph. A '''drawing''' of a graph $G$ is a drawing in $\mathbb{R}^2$ such that * the vertices of $G$ are distinct points, * the edges of $G$ are simple curves joining their endpoints, * no edge passes through a vertex, and * no three edges cross in a common point. The '''minimal crossing number''' of $G$ is then the minimal number of crossings of edges in a drawing of $G$. In particular, a graph is planar if and only if its minimal crossing number is $0$. It is moreover conjectured that the crossing number of the complete graph $K_n$ [1] is $$\frac{1}{4}\lfloor \frac{n}{2} \rfloor\lfloor \frac{n-1}{2} \rfloor\lfloor \frac{n-2}{2} \rfloor\lfloor \frac{n-3}{2} \rfloor,$$ and the crossing number of the complete bipartite graph $K_{n,m}$ [2] is $$\lfloor \frac{n}{2} \rfloor\lfloor \frac{n-1}{2} \rfloor\lfloor \frac{m}{2} \rfloor\lfloor \frac{m-1}{2} \rfloor.$$ A general algorithm to compute the crossing number is e.g. given in [3]. This statistics data was provided by Markus Chimani [6].

The minimal number of edges to add to make a graph Hamiltonian. A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.

The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.

The number of four-cliques in a graph.