The radius of a connected graph. This is the minimum eccentricity of any vertex.

The monochromatic index of a connected graph. This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path. For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.

The second Elser number of a connected graph. For a connected graph $G$ the $k$-th Elser number is $$els_k(G) = (-1)^{|V(G)|+1} \sum_N (-1)^{|E(N)|} |V(N)|^k$$ where the sum is over all nuclei of $G$, that is, the connected subgraphs of $G$ whose vertex set is a vertex cover of $G$. It is clear that this number is even. It was shown in [1] that it is non-negative.

The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.

The number of atoms of a lattice. An element of a lattice is an '''atom''' if it covers the least element.

The breadth of a lattice. The '''breadth''' of a lattice is the least integer $b$ such that any join $x_1\vee x_2\vee\cdots\vee x_n$, with $n > b$, can be expressed as a join over a proper subset of $\{x_1,x_2,\ldots,x_n\}$.