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Let X be a non-empty finite set, E be a finite dimensional euclidean vectorspace and G a finite subgroup of O(E), the orthognal group of E. SupposeGG={U_i | i in X} is a finite set of linear lines in E and an orbit of G onwhich its operation is twice transitive. Then GG is an equiangular set oflines, which means that we can find a real number "c", and generators u_i ofthe lines U_i (i in X) such that forall i,j in X, ||u_i||=1, and if i isdifferent from j then (u_i|u_j)=\gve_{i,j}.c, with \gve_{i,j} in {-1,+1\} LetGamma be the simple graph whose set of vertices is X, two of them, say i and j,being linked when \gve_{i,j} = -1. In this article we first explore therelationship between double transitivity of G and geometric properties ofGamma. Then we construct several graphs associated with a twice transitivegroup G, in particular any of Paley's graphs is associated with arepresentation of G=PSL_2(q) on a set of q+1 equiangular lines in a vectorspace whose dimension is (q+1)/2.

Groupes d'isom\'etries permutant doublement transitivement un ensemble de droites vectorielles