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

Local Large Deviation Principle, Large Deviation Principle and Information theory for the Signal -to- Interference -Plus- Noise Ratio Graph Models