From: Pre-emptive spectral graph protection strategies on multiplex social networks
Notation | Definition and description |
---|---|
G=(V,E_{1},…,E_{ L }) | Multiplex graph G with the node set V and the edge set E_{1,…,L} |
A | Multiplex supra adjacency matrix of graph G |
\(\mathcal {L}(A)\) | Combinatorial Laplacian matrix of A |
\(\mathcal {L}_{sym}(A)\) | Symmetric normalized Laplacian matrix of A |
\(\mathcal {L}_{rw}(A)\) | Random walk normalized Laplacian matrix of A |
n | Number of nodes in each multiplex layer |
m | Number of edges in each multiplex layer |
N | Number of nodes in graph G |
M | Number of edges in graph G |
L | Number of layers in graph G |
d(i) | Degree value (or outdegree value in directed graph) of node i |
PV(i) | Protection Value of node i |
α | Algebraic connectivity of \(\mathcal {L}_{rw}\) |
μ(i) | Corresponding Fiedler vector of \(\mathcal {L}_{rw}\) for node i |
β(i) | Infection probability at layer i |
δ(i) | Recovery probability at layer i |
ϕ | Number of initial infected nodes in a graph |
k | Number of available protection resources |
S | Set of nodes selected for protection |
η_{ G }(S) | Number of survived nodes of graph G at the end of epidemics |
θ_{ G }(S) | Percentage of survived nodes of graph G at the end of epidemics |
θ _{ ave } | Average of θ_{ G }(S) |
θ _{ std } | Standard deviation of θ_{ G }(S) |