Computing well-balanced spanning trees of unweighted networks

Šubelj, Lovro (author)

A spanning tree of a network or graph is a subgraph that connects all nodes with the minimum number or total weight of edges. Spanning trees are among the simplest yet most effective techniques for network simplification, sampling, and uncovering a network’s backbone or skeleton. Prim’s algorithm and Kruskal’s algorithm are well-known algorithms for computing a spanning tree of a weighted network, and are therefore also the default procedure for unweighted networks in the most popular network libraries. In this paper, we empirically evaluate the performance of these algorithms on unweighted networks and compare them with priority-first search algorithms. We show that the distances between the nodes are better preserved by a simpler algorithm based on breadth-first search. The spanning trees are also more compact and well-balanced, as measured by classical graph indices. We support our findings with experiments on synthetic graphs and over a thousand real networks, and demonstrate the practical applications of the computed spanning trees. We conclude that for preserving the structure of an unweighted network, the breadth-first search algorithm should be the preferred choice.

• Language: English
• Keywords: unweighted networks, spanning tree, breadth-first search, Prim’s algorithm, Kruskal’s algorithm
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 18 str.
• Numbering: Vol. 18, iss. 12, art. 760
• PID: 20.500.12556/RUL-176570
• UDC: 004.021
• ISSN on article: 1999-4893
• DOI: 10.3390/a18120760
• COBISS.SI-ID: 259877379
• Publication date in RUL: 04.12.2025

Record is a part of a journal

• Title: Algorithms
• Shortened title: Algorithms
• Publisher: MDPI
• ISSN: 1999-4893
• COBISS.SI-ID: 517501977

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: neutežena omrežja, vpeto drevo, preiskovanje v širino, Primov algoritem, Kruskalov algoritem

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P5-0168-2022
• Name: Družboslovna metodologija, statistika in informatika