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Table 1 Summary of terms and notations

From: Pre-emptive spectral graph protection strategies on multiplex social networks

Notation Definition and description
G=(V,E1,…,E L ) Multiplex graph G with the node set V and the edge set E1,…,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)