Minimum spanning trees on random networks

Details Minimum spanning trees on random networks Minimum spanning trees on random networks

2001-01-22

arxiv.org/abs/cond-mat/0101340v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.86.5076

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform disorder. We show that the MST energy for other disorder distributions is simply related to $P(\epsilon)$. We discuss the relationship to invasion percolation (IP), to the directed polymer in a random media (DPRM) and the implications for the broader issue of universality in disordered systems.

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