Računanje mjera centralnosti u velikim mrežama

master's thesis

• Title (english): Computing centrality measures in large networks
• Author: Bruno Fabulić
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-06, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U svijetu gdje smo svi povezani svakim danom sve više i više, nameće se zaključak da je proučavanje mreža vrlo bitan zadatak. Jedan od aspekata proučavanja mreža je određivanje mjera centralnosti koje pronalazi svakojake primjene. Za mjere centralnosti ne postoji jedna jedinstvena vijednost koja će nam reći koji je vrh najbitniji u mreži, nego postoji više različitih metoda koje možemo koristiti. Svaka metoda ima svoje karakteristike te na temelju njih odabiremo metodu koja nam najviše odgovare te zatim proučavamo dobivene rezultate. Predstavili smo četiri metode mjerenja centralnosti, to su: Page Rank, podgrafovska centralnost, Totalna komunikativnost i Katzova centralnost. Za svaku metodu naveli smo ideju iza nje, osnovne karakteristike, kako ju računamo te njene nedostatke. Za kraj, primjenili smo navedene metode na primjeru Marvelovog svijeta te dobili smislene rezultate.

Abstract (english)

In a world where we are connected with each other more and more by each day, the conclusion is that studying networks is a very important task. One of the aspects of studying networks is determining measures of centrality that find all kinds of applications in real world use-cases. For measures of centrality there does not exist one unique value that will tell us which vertex is the most important in the network, rather there are several different methods that we can use. Each method has its own characteristics and based on them we choose the method that suits us best and then we study the results obtained. We have presented four methods of measuring centrality, namely: Page rank, subgraph centrality, total subgraph communicability and Katz’s centrality. For each method we stated general ideas behind them, basic characteristics, how it’s calculated and their shortcomings. Finally, we applied mentioned methods to example of the Marvel world and got meaningful results.

• Keywords: proučavanje mreža; metode mjerenja centralnosti; Page Rank; podgrafovska centralnost; Totalna komunikativnost; Katzova centralnost.
• Keywords (english): studying networks; centrality measurement methods; Page Rank; subgraph centrality; total subgraph communicability; Katz's centrality
• Language: croatian
• URN:NBN: urn:nbn:hr:217:076208
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-24 12:18:01