A vertex subset S of a graph G is a global offensive alliance if every non-member v of S has at least as many neighbors inside S as outside S in the closed neighborhood of v. The global offensive alliance number \(\gamma _G\) is the cardinality of a minimal global offensive alliance. A vertex is a groupie if its degree is not less than the mean of the degrees of its neighbors. The number of groupies in G is denoted by \(\eta _G\) . In this paper, we study these two sort of orthogonal concepts over a heterogenous random graph G obtained by including each edge e from a complete graph \(K_n\) of order n with an individual probability \(p_n(e)\) independently. For a complete t-ary tree T with height 2, \(\gamma _T=\eta _T=t\) . In the random graph setting, it is found that \(\gamma _G\asymp \eta _G\asymp n/2\) under some neighborhood density conditions of the edge probabilities, where \(a_n\asymp b_n\) means \(a_n/b_n\rightarrow 1\) as \(n\rightarrow \infty \) .
