Connected component definition & meaning in DSA

Connected component in an undirected graph refers to a group of vertices that are connected to each other through edges, but not connected to other vertices outside the group.

For example in the graph shown below, {0, 1, 2} form a connected component and {3, 4} form another connected component.

Example of connected components

Characteristics of Connected Component:

• A connected component is a set of vertices in a graph that are connected to each other.
• A graph can have multiple connected components.
• Inside a component, each vertex is reachable from every other vertex in that component.

How to identify  Connected Component:

There are several algorithms to identify Connected Components in a graph. The most popular ones are:

• Depth-First Search (DFS)
• Breadth-First Search (BFS)
• Union-Find Algorithm (also known as Disjoint Set Union)

Applications of  Connected Component:

• Graph Theory: It is used to find subgraphs or clusters of nodes that are connected to each other.
• Computer Networks: It is used to discover clusters of nodes or devices that are linked and have similar qualities, such as bandwidth.
• Image Processing: Connected components also have usage in image processing.

What else can you read?

• Strongly Connected Components meaning in DSA
• Number of connected components of a graph
• Largest connected component on a grid