Table 1.
Notation.
| symbol | description |
|---|---|
| N | number of nodes in the network |
| M | maximum node degree |
| [k] | number of nodes of degree k (equal to ∑A [Ak]) |
| [kl] | number of pairs with one member having degree k, and with the other having degree l (equal to ∑A, B[AkBl) |
| n̄ | average degree distribution (equal to ∑kk[k]/N) |
| dk | proportion of nodes with degree k (equal to [k]/N) |
| 𝒞kl | correlation matrix between nodes of degree k and degree l |
| ϕ | clustering coefficient of the network (equal to the number of triangles divided by the number of triples) |
| [Ak] | number of nodes in state A with k neighbours |
| [A] | number of nodes in state A (equal to ∑k [Ak]) |
| [AkBl] | number of pairs with one member in state A and with degree k, and with the other member in state B and with degree l |
| [AkB] | number of pairs with one member in state A and with degree k, and with the other member in state B (equal to ∑l [AkBl]) |
| [AB] | number of pairs with one member in state A, and with the other member in state B (equal to ∑k [AkB]) |
| [AkBlCm] | number of triples with one edge member in state A and with degree k, with the middle member in state B and with degree l, and with the other edge member in state C and with degree m |
| θ(t) | the fraction of degree one nodes that remain susceptible at time t |
| Y(t) | auxiliary variable used in clustered PGF model (equal to ∑kk[Ik]) |
| g(x) | PGF for the network degree distribution (equal to ∑ dkxk) |
| τ | rate of transmission of infection across a network link |
| γ | rate of recovery from infection |