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master's thesis
Primjena teorije grafova u proučavanju mreža javnog prijevoza
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:867242
Mihaljević, Marija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Mihaljević, M. (2019). Primjena teorije grafova u proučavanju mreža javnog prijevoza (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:867242

Mihaljević, Marija. "Primjena teorije grafova u proučavanju mreža javnog prijevoza." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:867242

Mihaljević, Marija. "Primjena teorije grafova u proučavanju mreža javnog prijevoza." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:867242

Mihaljević, M. (2019). 'Primjena teorije grafova u proučavanju mreža javnog prijevoza', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:867242

Mihaljević M. Primjena teorije grafova u proučavanju mreža javnog prijevoza [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:867242

M. Mihaljević, "Primjena teorije grafova u proučavanju mreža javnog prijevoza", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:867242

Metadata
TitlePrimjena teorije grafova u proučavanju mreža javnog prijevoza
AuthorMarija Mihaljević
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu iznesene su osnovne definicije i rezultati vezani za mreže. Glavni dio teorije o mrežama je Teorem o maksimalnom toku i minimalnom rezu te Algoritam metode označavanja. Algoritmom metode označavanja konstruiramo niz tokova dane mreže rastuće vrijednosti, a izneseni teorijski rezultati osiguravaju da je posljednji tok u nizu maksimalan tok dane mreže. Teoremom o maksimalnom toku i minimalnom rezu dana je veza vrijednosti maksimalnog toka i kapaciteta minimalnog reza mreže. Preciznije, dokazano je da su te dvije veličine jednake. Zahvaljujući tom rezultatu, nakon primjene algoritma metode označavanja i određivanja maksimalnog toka mreže, lako se odredi i kapacitet minimalnog reza mreže. U drugom dijelu rada iznose se rezultati analize mreža javnog prijevoza Firence i Atike. Na primjeru tih mreža opisane su dvije vrste simulacije ciljanog napada na mreže javnog prijevoza: simulacija u statičnom i dinamičnom kontekstu. Takve simulacije omogućuju proučavanje ranjivosti mreže te, eventualno, pronalazak njezinih slabih točaka.
Abstract (english)
In this paper we presented the main definitions and results related to networks. The most important results related to network theory, in this paper, are the max-flow min-cut theorem and the labelling method algorithm. By the labelling method algorithm, the sequence of flows of increasing value is constructed and network theory ensures that algorithm terminates with the max-flow of a network. In the max-flow min-cut theorem, we can see relation between max-flow value and min-cut capacity of a network. To be more specific, it is proven that those two values are equal. This results ensure that if we apply the labelling method algorithm and find max-flow of a network, we can determine capacity of a min-cut. In the second part of this paper, the results of public transportation network analyses are shown. The analysis are based on two public transportation networks (PTNs), PTN of Florence and PTN of Attika region. In those analyses, two approaches in simulations of trageted attacks on PTNs are described: simulation in static context and simulation in dynamic context. Those simulations give us possibility to study vulnerability of PTNs and, eventually, determination of its weaknesses.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:867242
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-07-10 11:25:25