Algoritmi za štetje trikotnikov v grafu

ADAMIČ, JAN (author), Mihelič, Jurij (mentor)

Trikotniki v grafu so podgrafi, sestavljeni iz treh povezanih vozlišč. Število trikotnikov je računsko zahtevna statistika, ki se pogosto uporablja v analizi velikih omrežij in v raznih primerih uporabe, kot so recimo odkrivanje skupnosti v omrežju, zaznavanje vsiljive vsebine, odkrivanje skritih tematskih struktur. Cilj diplomskega dela je pregled in primerjava algoritmov za štetje trikotnikov. Na začetku predstavimo problem, definicije in nekaj primerov uporabe štetja trikotnikov. Nato predstavimo algoritme za točno štetje trikotnikov, zatem pa še algoritme za približno štetje. Na koncu sledi še primerjava hitrosti in kratek zaključek.

• Language: Slovenian
• Keywords: algoritem, graf, trikotniki, štetje
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2021
• PID: 20.500.12556/RUL-125365
• COBISS.SI-ID: 54953219
• Publication date in RUL: 12.03.2021

Secondary language

• Language: English
• Title: Algorithms for counting triangles in a graph

Abstract

Triangles in a graph are subgraphs composed of three connected nodes. The number of triangles is a computationally intensive statistic that is often used in the analysis of large networks and in various use cases, such as discovering communities in a network, detecting spam, discovering hidden thematic structures. The aim of the thesis is to review and compare algorithms for counting triangles. At the beginning we present the problem, definitions and some examples of the use of counting triangles. Then we present algorithms for exact counting of triangles, and then algorithms for approximate counting. Finally, there is a comparison of speed and a short conclusion.

• Keywords: algorithm, graph, triangle, counting