Let
G be a primitive strongly regular graph of order
n and
A is adjacency matrix.
In this paper we first associate to
A a real 3-dimensional Euclidean Jordan
algebra
![](//file.scirp.org/image/Edit_75bd0091-39f4-4458-aa67-df82664ff72c.bmp)
with rank three spanned by
In and the natural powers of
A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of
order
n. Next we consider a basis
![](//file.scirp.org/image/Edit_904a9615-b4d7-4c6d-814f-a12ddf902067.bmp)
that is a Jordan frame of
![](//file.scirp.org/image/Edit_b319e19f-df83-4daa-a428-8daf92c7f41d.bmp)
. Finally,
by an algebraic asymptotic analysis of the second spectral decomposition of
some Hadamard series associated to
A we establish some inequalities over the
spectra and over the parameters of a strongly regular graph.