A router topology is a graph with exact integer link weights. This lesson pins the graph that the rest of the book uses.

highlighted = computed this step

Why weights matter

A routing topology becomes a shortest-path problem when every link has a small integer weight.

V=6|V|=6
Weighted topologyThe router topology is validated as exact nonnegative integer-weighted edges.Weighted topology - weighted undirected topology4251035157ABCDEF

The pinned graph

This anchor graph has 6 routers and 9 undirected weighted links.

E=9|E|=9
Weighted topologyThe router topology is validated as exact nonnegative integer-weighted edges.Weighted topology - weighted undirected topology4251035157ABCDEF

Read one link both ways

The A-C link has weight 2. Because the topology is undirected, that same cost applies from C back to A.

w(A,C)=2w(A,C)=2
Weighted topologyThe router topology is validated as exact nonnegative integer-weighted edges.Weighted topology - weighted undirected topology4251035157ABCDEF

Start near A

From A, C has weight 2 while B has weight 4.

2<42<4
Weighted topologyThe router topology is validated as exact nonnegative integer-weighted edges.Weighted topology - weighted undirected topology4251035157ABCDEF

Use cost, not hop count

The path through C then D costs 2 plus 3, so D can be reached at 5 before the direct-looking B-D link with weight 10.

2+3=52+3=5
Weighted topologyThe router topology is validated as exact nonnegative integer-weighted edges.Weighted topology - weighted undirected topology4251035157ABCDEF

Summary

The graph is small and exact: routers are labels, links are undirected edges, and every displayed weight is an integer checked by the model.

weighted topology\text{weighted topology}
Weighted topologyThe router topology is validated as exact nonnegative integer-weighted edges.Weighted topology - weighted undirected topology4251035157ABCDEF