Math 2.0

definition

Connected graph

Definition

A graph GG is connected if its vertex set is nonempty and any two vertices of GG are reachable from each other.

Remarks

The empty graph, with no vertices, is not connected under this convention. Some authors call it connected. A graph is connected if and only if it has exactly one connected component. The cycle graphs, the path graphs and the trees are connected.

Explanations

L1 human

A graph is connected when it is in one piece. From any vertex you can reach any other vertex along edges.

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To read this node, read these 4 nodes in this order. The foundations come first, and the list ends with this node.

Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionReachability, definition, no evidence levelReachabilitydefinitionConnected graph, definition, no evidence levelConnected graphdefinition
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Graph definition
  2. Walk definition
  3. Reachability definition
  4. Connected graph definition

What depends on this

17 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Connectivity_(graph_theory), Connected vertices and graphs

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