  Let X be a non-empty finite set and alpha a symmetric bilinear form on a real
finite dimensional vector space E. We say that a set GG={U_i | i in X} of
linear lines in E is an isometric sheaf, if there exist generators u_i of the
lines U_i, and real constants ''omega'' and ''c '' such that : forall i,j in X,
alpha(u_i,u_i)=omega, and if i is different from j, then
alpha(u_i,u_j)=epsilon_{i,j}.c, with epsilon_i,j in {-1,+1} Let Gamma be the
graph whose set of vertices is X, two of them, say i and j, being linked when
epsilon_{i,j} = - 1. In this article we explore the relationship between GG and
Gamma ; we describe all sheaves associated with a given graph Gamma and
construct the group of isometries stabilizing one of those as an extension
group of Aut(Gamma). We finally illustrate our construction with some examples.
