a vertex is the fundamental unit of which graphs are formed.
two vertices are adjacent if they are connected by an edge.
we denote the set of edges belonging to a graph by . if we were to talk about a set of edges that dont necessarily belong to a specific graph, we simply write .
in a directed graph, the outdegree of a vertex is the number of the edges whose tail is connected to the vertex and the indegree is the number of edges whose head is connected to the vertex. the degree of a vertex is the total number of edges connected to it.