On the expressiveness and structural properties of centrality measures

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dc.catalogadorvdr
dc.contributor.advisorPieris, Andreas
dc.contributor.advisorRiveros Jaeger, Cristian
dc.contributor.authorSalas Cornejo, Jorge
dc.contributor.otherPontificia Universidad Católica de Chile. Escuela de Ingeniería
dc.date.accessioned2024-10-22T19:52:40Z
dc.date.available2024-10-22T19:52:40Z
dc.date.issued2024
dc.descriptionTesis (Doctor in Engineering Sciences)--Pontificia Universidad Católica de Chile, 2024
dc.descriptionTesis (Doctor of Philosophy)--Pontificia Universidad Católica de Chile, 2024
dc.description.abstractCentrality measures are used as analytical tools to understand graph-based data in various contexts. They are particularly useful for detecting important agents in disease spreading, influential individuals in social networks, or political decisionmakers. This is primarily due to the diversity of measures and their potential for exploitation in theoretical analyses. However, there exists a gap in the understanding of centrality from a foundational perspective. In this thesis, we provide an in-depth study of centrality measures from two different angles. Firstly, we examine how centralities behave over trees. Due to the simple structure of trees, it is easier to analyze each centrality measure in a restricted setting. We introduce the rooting tree property and propose a framework of potential functions to characterize rooting measures. In the last two Chapters, we present a novel study of the family of subgraph-based centralities (SBMs), which serve as a general framework for developing new measures. To define an SBM, we select a set of important subgraphs relevant to a specific application. The most important vertices are then determined based on the number of important subgraphs surrounding them. Initially, we investigate the absolute and ranking expressiveness of SBMs, answering the question of when an arbitrary centrality measure can be defined as an SBM. This, in turn, allows us to compare commonly used centralities within the scope of SBMs. Finally, we conduct an experimental study of important subgraph-based measures, as well as commonly used measures, using statistical scores such as Pearson correlation, ranking distances, and similarities to identify evidence of closely related measures.
dc.description.funderInstituto Milenio Fundamentos de los Datos (IMFD)
dc.fechaingreso.objetodigital2024-10-22
dc.format.extentxi, 187 páginas
dc.fuente.origenSRIA
dc.identifier.doi10.7764/tesisUC/ING/88328
dc.identifier.urihttps://doi.org/10.7764/tesisUC/ING/88328
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/88328
dc.information.autorucEscuela de Ingeniería; Riveros Jaeger, Cristian; 0000-0003-0832-116X; 131276
dc.information.autorucEscuela de Ingeniería; Salas Cornejo, Jorge; S/I; 223195
dc.language.isoen
dc.nota.accesocontenido completo
dc.rightsacceso abierto
dc.subjectCentrality measures
dc.subjectNetwork science
dc.subjectGraph data bases
dc.subject.ddc620
dc.subject.ddc100
dc.subject.deweyIngenieríaes_ES
dc.subject.ods16 Peace and Justice Strong Institutions
dc.subject.odspa16 Paz, justicia e instituciones sólidas
dc.titleOn the expressiveness and structural properties of centrality measures
dc.typetesis doctoral
sipa.codpersvinculados131276
sipa.codpersvinculados223195
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