—Many dynamical processes can be represented as directed attributed graphs or Petri nets where relationships between various entities are explicitly expressed. Signaling networks modeled as Petri nets are one class of such graphical models for representation. These networks encode how protein abundances in specific compartments, interact to create new protein products. Initially, proteins and rules governing their interactions are curated from literature and then refined with experimental data. Variation in these networks occurs at topological structure, size, and weights associated on edges. Collectively, these variations are quite significant for manual and interactive analyses. Furthermore, as new information is added to these networks, the emergence of new computational models becomes more significant. From this perspective, a hierarchical spectral decomposition method is proposed and applied for inferring similarities and dissimilarities from an ensemble of graphs that corre...