3 research outputs found

    Fundamental dynamics of popularity-similarity trajectories in real networks

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    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 H≪0.5H \ll 0.5. 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

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    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
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