Minimum weight spanning trees of weighted scale free networks

TL;DR

This paper investigates the structure of minimum weight spanning trees in weighted scale-free networks, analyzing how edge weight correlations affect the MST topology using Kruskal's algorithm.

Contribution

It provides insights into the sensitivity of MST structures to edge weight correlations in scale-free networks, a topic not extensively explored before.

Findings

MST structures vary with edge weight correlations.

Kruskal's algorithm effectively computes MSTs in scale-free networks.

The topology of MSTs reflects underlying network properties.

Abstract

In this lecture we will consider the minimum weight spanning tree (MST) problem, i.e., one of the simplest and most vital combinatorial optimization problems. We will discuss a particular greedy algorithm that allows to compute a MST for undirected weighted graphs, namely Kruskal's algorithm, and we will study the structure of MSTs obtained for weighted scale free random graphs. This is meant to clarify whether the structure of MSTs is sensitive to correlations between edge weights and topology of the underlying scale free graphs.