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A subgraph, also known as a partial graph or induced subgraph, is a graph derived from another graph by deleting some of its vertices and edges. In other words, a subgraph is a subset of the vertices and edges of a graph, where the edges in the subgraph are the same as in the original graph but restricted to the subset of vertices.

Subgraphs can be classified into two main types:

1. Induced Subgraph: This is a subgraph that includes all the edges of the original graph that connect the vertices in the subgraph. In other words, if two vertices in the subgraph are connected by an edge in the original graph, that edge is also included in the subgraph.

2. Non-Induced Subgraph: This is a subgraph that may not include all the edges of the original graph that connect the vertices in the subgraph. In other words, some edges may be omitted from the subgraph.

Subgraphs are a fundamental concept in graph theory and have numerous applications in various fields such as computer science, network analysis, and social sciences. They are used to model and analyze complex systems, where the system is represented as a graph and the subgraphs represent subsets of the system.