Simplicial Complexes From Graphs Toward Graph Persistence

Zuffi, Lorenzo (2017) Simplicial Complexes From Graphs Toward Graph Persistence. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Zuffi, Lorenzo
Relatore della tesi
Correlatore della tesi
Corso di studio
Curriculum A: Generale e applicativo
Ordinamento Cds
Parole chiave
persistent homology graph theory simplicial complexes graphs graph complexes algebraic topology computational topology
Data di discussione della Tesi
31 Marzo 2017

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