Special types of Graph
Types of Graph
- A tree is a connected graph with no cycles and one less arc than nodes.
- A spanning tree of Graph G (where G is a full graph, not a tree) is a subgraph which includes all the vertices of G and is also a tree.
- A complete network is a network where each node is directly connected to every other node in the network.
- On a connected graph, you can get from one node to any other node, but not necessarily directly.
- Isomorphic graphs are graphs that show the same information, but are drawn in a different way.
A complete network is a network where each node is directly connected to every other node in the network.
Info
Notation Kn is the complete network of n number of nodes.
The sequence for the number of arcs in a complete network is basically factorial with addition. (aka \(\sum_{r=1}^{n}r=1+2+3+\dots+n = \frac{n\times (n+1)}{2}\))
One way of thinking about this is that an arc has two endings, therefore you can do Number of nodes in network x Number of nodes in network -1, all divided by 2.
This gives the same answer.