Graphs can be of several types.

Basic Graphs

  • A graph with only arcs is called a directed graph, while a graph with no arcs is called a non-directed graph. A graph with both arcs and non-directed edges is called a mixed graph.

  • A null graph is a graph that has no vertices or edges.

  • A trivial graph is a graph that consists of a single vertex with no edges.

  • A proper graph is a graph with an edge that joins two different vertices.

  • A general graph (or pseudo-graph) is a graph that consists of at least one loop or at least one multi-edge.

  • A multi-graph (or loop-less graph) is a graph that has at least one multi-edge, but no loops.

Elegant Graphs

Connected Graphs

Bipartite Graphs

  • A bipartite graph is a graph that can be “separated” into two interconnected graphs

    • A complete bipartite graph is a bipartite graph where all the vertices of each subgraph are connected between each other.


A subgraph is a graph contained within another graph.

When we erase most of the edges in a subgraph while keeping only the necessary ones to join all the vertices, we get an expanded subgraph.