Some excerpts from the article
Comparing methods for comparing networks Scientific Reports volume 9, Article number: 17557 (2019)
By Mattia Tantardini, Francesca Ieva, Lucia Tajoli & Carlo Piccard
are:
To effectively compare networks, we need to move to inexact graph matching, i.e., define a real-valued distance which, as a minimal requirement, has the property of converging to zero as the networks approach isomorphism.
we expect that whatever distance we use, it should tend to zero when the perturbations tend to zero
the diameter distance, which remains zero on a broad range of perturbations for most network models, thus proving inadequate as a network distance
Virtually all methods demonstrated a fairly good behaviour under perturbation tests (the diameter distance being the only exception), in the sense that all distances tend to zero as the similarity of the networks increases.
If achieving thermodynamic efficiency is the benchmark criterion for all kinds of networks, then their topologies should converge to the same model. If they all converge to the same model when optimally efficient, does that cast doubt on topology as a way to evaluate and differentiate networks?
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