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A graph where the edges have a direction associated with them. Each edge is an ordered pair of vertices.

A graph in which edges have no direction. Each edge is an unordered pair of vertices.

A graph with numbers (weights) assigned to its edges. These weights represent cost, distance, or any other quantifiable metric.

An undirected graph with no loops (edges connected at both ends to the same vertex) and no more than one edge between any two vertices.

A simple graph in which every pair of distinct vertices is connected by a unique edge.

A graph whose vertices can be divided into two disjoint sets $U$ and $V$ such that every edge connects a vertex in $U$ to one in $V$. There are no edges between vertices of the same set.

A graph that contains at least one graph cycle. A cycle is a path of edges and vertices wherein a vertex is reachable from itself.

A graph with no cycles. If directed, it is known as a Directed Acyclic Graph (DAG).

An undirected graph in which there exists a path between every pair of vertices.