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

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

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

A graph which may have multiple edges (also called parallel edges) between two nodes. These edges could be both directed and undirected.

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

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