  We present a methodological framework for studying galaxy evolution by
utilizing Graph Theory and network analysis tools. We study the evolutionary
processes of local ultraluminous infrared galaxies (ULIRGs) and quasars and the
underlying physical processes, such as star formation and active galactic
nucleus (AGN) activity, through the application of Graph Theoretical analysis
tools. We extract, process and analyse mid-infrared spectra of local (z < 0.4)
ULIRGs and quasars between 5-38 microns through internally developed Python
routines, in order to generate similarity graphs, with the nodes representing
ULIRGs being grouped together based on the similarity of their spectra.
Additionally, we extract and compare physical features from the mid-IR spectra,
such as the polycyclic aromatic hydrocarbons (PAHs) emission and silicate depth
absorption features, as indicators of the presence of star-forming regions and
obscuring dust, in order to understand the underlying physical mechanisms of
each evolutionary stage of ULIRGs. Our analysis identifies five groups of local
ULIRGs based on their mid-IR spectra, which is quite consistent with the well
established fork classification diagram by providing a higher level
classification. We demonstrate how graph clustering algorithms and network
analysis tools can be utilized as unsupervised learning techniques for
revealing direct or indirect relations between various galaxy properties and
evolutionary stages, which provides an alternative methodology to previous
works for classification in galaxy evolution. Additionally, our methodology
compares the output of several graph clustering algorithms in order to
demonstrate the best-performing Graph Theoretical tools for studying galaxy
evolution.
