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Table 1 Frequently used notation

From: Non-submodular model for group profit maximization problem in social networks

Notation Description
\(G=(V,E,P)\) A social network with user set V and edge set E. P is the influence probability. \(P_e\) represents influence probability on edge e where \(0\le P_e\le 1\)
\(G=(V,C,E,P,f)\) A candidate seed set \(C\subseteq V\). Each user has a weight f
\({\mathcal {U}}\) The set of groups, b(U) is the benefit when U is activated for \(U\in {\mathcal {U}}\)
\(c(v)\ge 0\) c(v) is the cost to activate v
\(n=|V|\) The number of users
\(m=|E|\) The number of edges
\(l=|{\mathcal {U}}|\) The number of groups
\(\beta\) The threshold of a group being activated, \(0<\beta \le 1\)
k The number of seeds
\(\beta (S)\) The expected benefit of all activated groups with seed set S.
\(\gamma (S)\) The expected diffusion cost of all activated users with seed set S
\(\rho (S)=\beta (S)-\gamma (S)\) The expected profit with seed set S