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The number of edges incident to the vertex. For a vertex $v$, this is written as $deg(v)$.

The minimum eccentricity of any vertex in the graph. For graph $G$, $radius(G) = \min_{u \in V(G)} \max_{v \in V(G)} d(u,v)$.

The number of edges in a cycle within a graph.

The longest shortest path between any two vertices in a graph. For graph $G$, $diameter(G) = \max_{u,v \in V(G)} d(u,v)$ where $d(u,v)$ is the shortest path between $u$ and $v$.

The smallest number of colors needed to color the vertices of a graph so that no two adjacent vertices share the same color.

A circuit in a graph that visits every edge exactly once. A connected graph has an Eulerian circuit if and only if every vertex has an even degree.

The greatest possible flow from the source to the sink in a network with capacities. It can be calculated using algorithms like Ford-Fulkerson method.

A path in a graph that visits each vertex exactly once. Determining if such a path exists is known as the Hamiltonian Path Problem.

A square matrix $A$ used to represent a finite graph. The elements $A_{ij}$ are $1$ if there is an edge between vertices $i$ and $j$, and $0$ otherwise.

A measure of the degree to which all vertices of a graph are connected. A graph is 'k-connected' if there are at least 'k' vertex-disjoint paths between any two vertices.

A matrix $B$ that shows the relationship between vertices and edges. For a graph $G$ with $V$ vertices and $E$ edges, $B$ is a $V \times E$ matrix where $B_{ve} = 1$ if vertex $v$ is incident to edge $e$, otherwise $B_{ve} = 0$.