In this note, we describe a methodology for comparing networks represented as weighted graphs. The key idea is to associate a probability density function derived from the graph Laplacian, and then compute the Wasserstein distance between the derived densities of the respective graphs. While previous work has focused on network geometry (curvature-based) measures for edges (Ricci) and nodes (scalar), there remains a need to develop a global similarity across time-varying networks. We note that this paper should be read as a note and is presented with very preliminary results; it sets the foundation for other investigations that are currently on-going. This said, we provide network similarity results across synthetic toy results to empirically illuminate the proposed method.