Simple graph

A simple graph is a set of vertices joined by edges, with no edge joining a vertex to itself and at most one edge between any pair of vertices.

Graph theory: The mathematical study of structures formed from vertices and edges. Simple graphs are a foundational kind of object in this field.
Adjacency matrix: A matrix whose entries record which pairs of vertices in a graph are adjacent. For a simple graph, its adjacency matrix is symmetric with a zero diagonal.
Multigraph: A graph-like structure that permits multiple edges between the same pair of vertices. It differs from a simple graph by allowing parallel edges.
Social network: A network representing social entities and the relationships among them. A simple graph can encode undirected, unweighted relationships between pairs of people.
Vertex (graph theory): An element of a graph's vertex set, representing an object or location. A simple graph's vertices are the endpoints that its edges may join.
Incidence matrix: A matrix recording which vertices are incident to which edges. It represents the vertex-edge relationships of a simple graph.
Pseudograph: A graph-like structure that permits loops and may permit multiple edges. It relaxes both restrictions that distinguish simple graphs.
Molecular graph: A graph representation of a molecule in which atoms are vertices and bonds are edges. It uses graph structure to represent pairwise chemical bonds.
Edge (graph theory): A connection between two vertices in a graph. The absence of loops and duplicate edges constrains which edges are allowed.
Complete graph: A simple graph in which every pair of distinct vertices is joined by an edge. It is the maximally connected simple graph on a fixed number of vertices.

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