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Table 1 Summary of Symbols and Notations

From: Effective and scalable methods for graph protection strategies against epidemics on dynamic networks

Notation Definition and description
GD=(VD,ED) dynamic network GD with the node set VD and the edge set ED
G t snapshot of dynamic network GD at time t
k protection budget, i.e., the number of nodes in graph GD that can be protected
S set of k nodes selected for protection
N number of nodes in graph GD
M number of edges in graph GD
β infection rate
δ recovery rate
θ ratio of surviving nodes in graph GD at the end of epidemics
w(u,v) edge weight between node u and v
V c vertex cover of graph Gt
\(V_{c}^{*}\) minimum vertex cover of graph Gt
\(\mathbb {S}\) current partial solution, set of selected \(V_{c}^{*}\) nodes of graph Gt
d size of embedding vector dimension
\(h(\mathbb {S})\) feature-based representation of \(\mathbb {S}\) in d-dimensional vector
B batch samples of training
\(\mathbb {M}\) experience replay memory of n-step fitted Q-Learning
ψ i set of neural network parameters (weights) of respective embedding variable i
Ψ collection of neural network’s set of parameters (weights) \(\Psi = \{\psi _{i}\}_{i=1}^{7}\)