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 modeling and representations. These networks encode how different protein in specific compartments, interact to create new protein products. Initially, the proteins and rules governing their interactions are curated from literature and then refined with experimental data. Variation in these networks occurs in topological structure, size, and weights associated on edges. Collectively, these variations are quite significant for manual and interactive analysis. Furthermore, as new information is added to these networks, the emergence of new computational models becomes paramount. From this perspective, hierarchical spectral methods are proposed and applied for inferring similarities and dissimilarities from an ensemble of graphs that corresponds to reaction networks. The technique has been implemented and tested on curated signaling networks that are derived for breast cancer cell lines.