In this paper, we establish a graph imaging technique to manifest local stabilization within atomic systems of multilevel atoms. Specifically, we address the interrelation between local stabilization and image entropy. As an example, we consider the mutual interaction of two-pair of pulses propagation in a double-Λ configuration as a dynamical graph-model with four nodes. The dynamic transition-matrix describes the connectivity matrix in the static graph-modal. Recently, we have obtained the transition matrix associated with the graph-model for the light interaction with multilevel atoms [1]. It is to be emphasized that the graph and its image have the same transition matrix. Mainly, the graph-model exposes the stabilization in terms of the singular-value decomposition of energies for the transition matrix. That is, and irrespective of the structure of the transition matrix. The image-model of the graph displays the details of the matrix structure in terms of rows and columns probabilities. Therefore, it will enable us to study conditional probabilities and mutual information inherent in the network of the graph. Furthermore, the graph imaging provides the main row/column contribution to the transition-matrix in terms of image entropy. Our results show that image entropy exposes spatial dependence which is irrelevant to graph entropy.

[1] Alhasan, A.M. Graph Entropy Associated with Multilevel Atomic Excitation. Proceedings 2020, 46(1), 9.