Math 2.0

Combinatorics Definition

Connected component

Builds on Reachability

Definition

Let GG be a graph. A connected component of GG is an equivalence class of the vertices of GG under reachability. The subgraph induced by a connected component is also called a connected component.

Remarks

The connected components partition the vertex set. Each component, as an induced subgraph, is connected. A graph with nn vertices and mm edges has at least n−mn - m components. A graph with no edges on nn vertices has nn components.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionReachability, definition, no evidence levelReachabilitydefinitionConnected component, definition, no evidence levelConnected componentdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Graph definition
  2. Walk definition
  3. Reachability definition
  4. Connected component definition

Where this leads

5 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Component_(graph_theory), Definitions and examples
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