For a finite typed graph on $n$ nodes and with type law $μ,$ we define the so-called spectral potential $ρ_λ(\,\cdot,\,μ),$ of the graph.From the $ρ_λ(\,\cdot,\,μ)$ we obtain Kullback action or the deviation function, $\mathcal{H}_λ(π\,\|\,ν),$ with respect to an empirical pair measure, $π,$ as the Legendre dual. For the finite typed random graph conditioned to have an empirical link measure $π$ and empirical type measure $μ$, we prove a Local large deviation principle (LLDP), with rate function $\mathcal{H}_λ(π\,\|\,ν)$ and speed $n.$ We deduce from this LLDP, a full conditional large deviation principle and a weak variant of the classical McMillian Theorem for the typed random graphs. Given the typical empirical link measure, $λμ\otimesμ,$ the number of typed random graphs is approximately equal $e^{n\|λμ\otimesμ\|H\big(λμ\otimesμ/\|λμ\otimesμ\|\big)}.$ Note that we do not require any topological restrictions on the space of finite graphs for these LLDPs.