  Given devices space $D$, an intensity measure $\lambda m\in(0,\infty)$, a
transition kernel $Q$ from the space $D$ to positive real numbers $(0,\infty,$
a path-loss function (which depends on the Euclidean distance between the
devices and a positive constant $\alpha$), we define a Marked Poisson Point
process (MPPP). For a given MPPP and technical constants
$\tau_{\lambda},\gamma_{\lambda}:(0,\,\infty)\to (0,\infty),$ we define a
Marked Signal-to- Interference and Noise Ratio (SINR) graph, and associate with
it two empirical measures; the \emph{empirical marked measure} and the
\emph{empirical connectivity measure}. For a class of marked SINR graphs, we
prove a joint \emph{ large deviation principle}(LDP) for these empirical
measures, with speed $\lambda$ in the $\tau$-topology. From the joint large
deviation principle for the empirical marked measure and the empirical
connectivity measure, we obtain an Asymptotic Equipartition Property(AEP) for
network structured data modelled as a marked SINR graph. Specifically, we show
that for large dense marked SINR graph one require approximately about
$\lambda^{2}H(Q\times Q)/\log 2$ bits to transmit the information contained in
the network with high probability, where $ H(Q\times Q)$ is a properly defined
entropy for the exponential transition kernel with parameter $c$.
  Further, we prove a \emph {local large deviation principle} (LLDP) for the
class of marked SINR graphs on $D,$ where
$\lambda[\tau_{\lambda}(a)\gamma_{\lambda}(a)+\lambda\tau_{\lambda}(b)\gamma_{\lambda}(b)]\to
\beta(a,b),$ $ a,b\in (0,\infty)$, with speed $\lambda$ from a \emph{ spectral
potential} point. From the LLDP we derive a conditional LDP for the marked SINR
graphs.
