Table 1 Notation
From: An analytical solution to the multicommodity network flow problem with weighted random routing
G | \(G(N,E) \text { is a graph with } N \text { nodes and } E \text { edges}\) |
A | \((A_{ij}) \text { is the weighted adjacency matrix with } A_{ii} = 0, A_{ij} \ge 0 \text { for all } i,j \le N\) |
\(d_i\) | \(\sum _j A_{ij} \text { is the degree of node } i \le N\) |
D | \((d_i) \text { is the } N \times N \text { diagonal matrix of weighted nodal degrees}\) |
L | \(D-A \text { is the graph Laplacian }\) |
M | \((M_{ij}) = L+ \mathbf{1} _{N \times N}/N \text { is the uniformly perturbed graph Laplacian }\) |
T | \((T_{ij}) \text { is the } N \times N \text { demand matrix}\) |
\({\tilde{T}}\) | \(\text { diagonal matrix of nodal demands} \,\,{\tilde{T}}_j = \sum _i T_{ij}\) |
\(L_T\) | \({\tilde{T}}- T \text { is the demand Laplacian for symmetric}\ T\) |