Web Reference: The components of a graph can be constructed in linear time, and a special case of the problem, connected-component labeling, is a basic technique in image analysis. Dynamic connectivity algorithms maintain components as edges are inserted or deleted in a graph, in low time per change. Intuitively, a connected component is a “piece” of a graph in the sense we just talked about. Question: How do we know that this particular definition of a “piece” of a graph is a good one? Goal: Prove that any graph can be broken apart into dif erent connected components. In graph theory, a component is a subgraph in which any two vertices are connected to each other by paths, either directly or indirectly, and are not connected to any other vertices in the supergraph.
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