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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 \((T_{ij}) \text { is the } N \times N \text { demand matrix}\)
\({\tilde{T}}\) \(\text { diagonal matrix of nodal demands} \,\,{\tilde{T}}_j = \sum _i T_{ij}\)
\(L_T\) \({\tilde{T}}- T \text { is the demand Laplacian for symmetric}\ T\)