Counting Connected Components in an Undirected Graph

We're given a graph of $n$ nodes and an array of edges belonging to this graph. Every edge is undirected and connects two nodes $a$ and $b$. We need to return the number of connected components in the graph.

In this problem, we are tasked with determining the number of connected components in an undirected graph. Connected components in a graph are subgraphs where any two vertices are connected to each other by paths, and which are connected to no additional vertices in the supergraph. Understanding connected components is fundamental in graph theory as it helps in breaking down a graph into its independent substructures.

To solve this problem, one efficient method is to employ Depth First Search (DFS) or Breadth First Search (BFS). These graph traversal algorithms help in visiting all the nodes in each connected component once. By iteratively running one of these algorithms on unvisited nodes, we can count the connected components. Every initiation of a traversal on an unvisited node signifies the discovery of a new connected component.

Conceptually, this problem is related to exploring the structural properties of graphs and employing graph traversal techniques. It helps in understanding how different nodes in a graph relate to each other and how we can systematically explore interconnected structures. Recognizing connected components is crucial for more advanced topics in graph theory and is a foundational skill in analyzing and solving graph-based problems.