Lalli, Margherita
(2024)
*Scale-Invariant Random Graphs: a multiscale approach to network modeling.*
Advisor: Garlaschelli, Prof. Diego. pp. 170.
[IMT PhD Thesis]

Text (Doctoral thesis)
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## Abstract

In the last decades, consistent efforts have been spent to capture specific shades of real systems through the development of random graph models, which have been studied extensively either for their practical value as statistical benchmarks and their theoretical appeal, as abstract tools capable of generating synthetic graphs with realistic properties. In particular, establishing a robust representation of a graph at multiple scales of observation would enable considerable progress in the description, modeling, and control of realworld complex systems. Here, by building on the principles of renormalization group theory from statistical mechanics, we derive a random graph model precisely conceived to provide a statistically consistent description of a network for different resolutions of its units and in an exact manner. We explore two interesting facets of the proposed model, which interlace with different branches of network science. On the one hand, it allows complying with empirical networks to provide up-scaled and down-scaled reconstructions according to a chosen hierarchy of partitions of the original nodes. In this sense, the model constitutes solid support for harboring a coarse-graining scheme of real systems without relying on any arbitrary introduction of a metric space. Secondly, this scale-invariant random graph itself turns out to generate networks with topological properties that are widespread among real-world systems and thus its mathematical sifting has its own theoretical interest.

Item Type: | IMT PhD Thesis |
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

PhD Course: | Computer science and systems engineering |

Identification Number: | https://doi.org/10.13118/imtlucca/e-theses/414 |

NBN Number: | urn:nbn:it:imtlucca-30037 |

Date Deposited: | 15 May 2024 10:45 |

URI: | http://e-theses.imtlucca.it/id/eprint/414 |

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