3 research outputs found
Fundamental dynamics of popularity-similarity trajectories in real networks
Real networks are complex dynamical systems, evolving over time with the
addition and deletion of nodes and links. Currently, there exists no principled
mathematical theory for their dynamics -- a grand-challenge open problem in
complex networks. Here, we show that the popularity and similarity trajectories
of nodes in hyperbolic embeddings of different real networks manifest universal
self-similar properties with typical Hurst exponents . This means
that the trajectories are anti-persistent or 'mean-reverting' with short-term
memory, and they can be adequately captured by a fractional Brownian motion
process. The observed behavior can be qualitatively reproduced in synthetic
networks that possess a latent geometric space, but not in networks that lack
such space, suggesting that the observed subdiffusive dynamics are inherently
linked to the hidden geometry of real networks. These results set the
foundations for rigorous mathematical machinery for describing and predicting
real network dynamics
Graph Theoretical Analysis of local ultraluminous infrared galaxies and quasars
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.Comment: Accepted for publication in Astronomy and Computin