Editing Scale-free network (section)

==Overview==
When the concept of "scale-free" was initially introduced in the context of networks,<ref name="Emergence of scaling in random netw"/> it primarily referred to a specific trait: a power-law distribution for a given variable <math>k</math>, expressed as <math>f(k)\propto k^{-\gamma}</math>. This property maintains its form when subjected to a continuous scale transformation <math>k\to k+\epsilon k</math>, evoking parallels with the renormalization group techniques in statistical field theory.<ref name="stat-field-theor-1">{{Cite book
 | last1 = Itzykson
 | first1 = Claude
 | last2 = Drouffe
 | first2 = Jean-Michel
 | title = Statistical Field Theory: Volume 1, From Brownian Motion to Renormalization and Lattice Gauge Theory
 | year = 1989
 | edition = 1st
 | publisher = Cambridge University Press
 | location = New York
 | isbn = 978-0-521-34058-8
 | language = English
}}
</ref><ref name="stat-field-theor-2">{{Cite book
 | last1 = Itzykson
 | first1 = Claude
 | last2 = Drouffe
 | first2 = Jean-Michel
 | title = Statistical Field Theory: Volume 2, Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems
 | year = 1989
 | edition = 1st
 | publisher = Cambridge University Press
 | location = New York
 | isbn = 978-0-521-37012-7
 | language = English
}}
</ref>

However, there's a key difference. In statistical field theory, the term "scale" often pertains to system size. In the realm of networks, "scale" <math>k</math> is a measure of connectivity, generally quantified by a node's degree—that is, the number of links attached to it. Networks featuring a higher number of high-degree nodes are deemed to have greater connectivity.

The power-law degree distribution enables us to make "scale-free" assertions about the prevalence of high-degree nodes.<ref name="scale-free_mz23">{{Cite journal
 | last1 = Meng
 | first1 = Xiangyi
 | last2 = Zhou
 | first2 = Bin
 | title = Scale-Free Networks beyond Power-Law Degree Distribution
 | year = 2023
 | journal = Chaos, Solitons & Fractals
 | volume = 176
 | pages = 114173
 | doi = 10.1016/j.chaos.2023.114173
| arxiv = 2310.08110
 | bibcode = 2023CSF...17614173M
 | s2cid = 263909425
 }}</ref> For instance, we can say that "nodes with triple the average connectivity occur half as frequently as nodes with average connectivity". The specific numerical value of what constitutes "average connectivity" becomes irrelevant, whether it's a hundred or a million.<ref name="scale-free_t05">{{Cite journal
 | last = Tanaka
 | first = Reiko
 | title = Scale-Rich Metabolic Networks
 | year = 2005
 | journal = Phys. Rev. Lett.
 | volume = 94
 | issue = 16
 | pages = 168101
| doi = 10.1103/PhysRevLett.94.168101
 | pmid = 15904266
 | bibcode = 2005PhRvL..94p8101T
 }}
</ref>