What is a component, in graph theory, if you want to define it in a paper?
2026-04-03 04:03:19.1775188999
What is academic definition of "Component" in graph theory? what is it?
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Well, one can define ''component'' as follows.
Define a binary relation on the nodes of an undirected graph by saying that two nodes $u,v$ are connected if there a path in the graph between $u$ and $v$.
This is an equivalence relation (transitive, reflexive, symmetric) on the node set.
The equivalence class containing the node $v$ is the set of all nodes which are connected to $v$ by paths in the graph. This equivalence class is the component of the graph containing $v$.
The graph consists of a set of (disjoint) components (equivalence classes).