Talk:Scale-free network

message: This is my first time using the talk page, so please forgive any missed wikiquette.
The article was most helpful to me, however I am curious about one thing.  Why are these networks called "scale free"?  I assume that this is a reference to self-similarity, but what exactly is self-similar in a scale-free network?  The sample diagrams of networks I have seen are not obviously fractal.  
David M.
:scale-free is not self-similar. Scale-free (as I understand it) is that there is no meaningful "average" for the behavior of the system. ChaTo 17:19, 12 December 2005 (UTC)
replies: text: For the old definition of Scale-free this was true, but the Lun Li definition actually includes the concept of self-similarity. Meekohi 15:34, 13 December 2005 (UTC)

text: As I understand it, the term "scale-free" is closely related to the term "scale-invariant", which is perhaps a more intuitive phrase. It means (roughly) that regardless of how much you "zoom in or out", the structure is going to look essentially the same. Kmote (talk) 21:05, 8 October 2008 (UTC)
replies: text: I was only partially correct. Here is the real answer, as described by Barabasi himself (in "Linked: The New Science of Networks", Basic Books, 2003, p.70): "The power law distribution thus forces us to abandon the idea of a scale, or a characteristic node. In a continuous hierarchy there is no single node which we could pick out and claim to be characteristic of all the nodes. There is no intrinsic scale in these networks. This is the reason my research group started to describe networks with power-law degree distribution as scale-free." Kmote (talk) 15:58, 13 October 2008 (UTC)
thread_title:  The name "scale free" 

message: Please forgive me if I am mistaken, but on reading, 'the authors...', it seems that an original viewpoint is being expounded, I thought that this was against Wikipedian principles of no new or original research being included?
Jim lewis1 (talk) 22:28, 3 April 2008 (UTC)
replies: text: I believe "the authors..." refers to Pennock et al., rather than to the authors of the wikipedia article, I have changed "the authors..." to "they" in order to make this clearer Echinoidea (talk) 21:09, 2 September 2008 (UTC)
thread_title:  Original research, against Wikipedia guidelines? 

message: The figures shows a directed graph, but the text does not mention directed graphs. the reader will ask herself. What is the meaning of the arrows? Must a hub necesarily be a source? etc..
:Agreed. I'll contact the original artist and ask if he wouldn't mind making the modification, I think having a figure is very useful for people seeing this for the first time. Meekohi 14:05, 12 December 2005 (UTC)
replies: text: changed to undirected graph, thank you for contacting me Meekohi. The source of this image is my Ph.D. thesis on web crawling: (Carlos Castillo: "Efficient Web Crawling". PhD Thesis. Universidad de Chile, 2004.) ChaTo 17:15, 12 December 2005 (UTC)
thread_title:  Confusing figure (fixed) 

message: The figure labeled "Complex network degree distribution of random and scale-free" has two curves.  Presumably one (I'm guessing the one with the semi-normal distribution) is for random networks, the other for scale-free networks.  Can the curves be labeled, or otherwise distinguished?  (Also, the label is odd--not quite English.  Maybe "Complex degree distribution of random and scale-free networks"? Although I'm not sure what "complex" has to do with it.) Mcswell (talk) 17:07, 2 July 2014 (UTC)
thread_title:  Confusing figure (not yet fixed) 

message: Probably silly question, but if "This model was originally discovered by Derek de Solla Price in 1965 under the term cumulative advantage", how was it "further developed by Herbet Simon in the 1950s"? Mmt 03:12, 5 April 2006 (UTC)
replies: text: Sounds like a pretty good question to me actually. Does anyone have a source for this Herbert Simon? I've never heard of him before. Meekohi 03:26, 5 April 2006 (UTC)

text: Part of the problem was a typo. Should have been Herbert Simon, but the dates still make no sense so I took that part out of the article for now. Meekohi 03:30, 5 April 2006 (UTC)
thread_title: History

message: Now define
 S(g) = \frac{s(g)}{s_{max}} 
where smax is the maximum value of s(h) for h in the set of all graphs with an identical degree distribution to g. 
I was wondering. What is an identical degree distribution? Is the amount of vertices of a certain degree exactly the same across these identical distributions? Or is the power-law exponent exactly the same? Or are they all power-law distributions or Poisson distributions? Andy 10:53, 6 October 2006 (UTC)
thread_title:  Identical degree distribution 

message: In the entry for Derek J. de Solla Price, it says that his contribution was "his interpretation of Herbert Simon's theory on cumulative advantage processes, or Robert K. Merton's Matthew effect, respectively (Price 1976)." So shouldn't Simon or Merton be credited with the discovery? --Nick 17:05, 1 December 2006 (UTC)
replies: text: Sounds reasonable to me, but someone should track down a source for this before making a final statement about it probably. Meekohi 04:49, 3 December 2006 (UTC)
thread_title:  Derek de Solla Price did not "Discover" Cumulative Advantage 

message: To their surprise, the Web did not have an even distribution of connectivity. Why is this surprising? Kope (talk) 19:42, 18 June 2008 (UTC)
thread_title:  Web is not random 

message: This article has a lot of references, but it's more like a paper article in that there are no links from the text to the reference section. - Dougher (talk) 02:02, 24 February 2009 (UTC)
thread_title:  No links from text to references 

message: It may not merit mention in the article, but I think it is interesting that perhaps the earliest reference to scale free phenomenon is recorded in Luke 19:26:   
    
:"[Jesus] replied, 'I tell you that to everyone who has, more will be given, but as for the one who has nothing, even what he has will be taken away." 
Perhaps if other references could be compiled from antiquity, it might be worthy of a small section. (Of course, I'm not suggesting that Jesus had anything like social network dynamics in mind when he uttered this, but the reference seems striking to me in this context.) Kmote (talk) 21:02, 17 August 2010 (UTC)
thread_title:  Reference from Antiquity 

message: I'm a little worried about characterizing the degree distribution as a power law; in the original BA paper, if I'm correct,  they used a least-squares linear regression which is a no-no (see http://arxiv.org/abs/0706.1062). It has been argued that the distribution of web links more closely follows a log-normal distribution. Before I change this, am I completely off base here?  — Preceding unsigned comment added by Octochimps (talk • contribs) 16:05, 7 February 2011 (UTC)
thread_title:  Power law versus logNormal 

message: I think that Generalized scale-free model should be merged into Scale-free network#Generative models, as the former is fairly short and doesn't seem like it could/should be a substantive article on its own. Joe SchmedleyTalk 15:59, 21 August 2011 (UTC)
thread_title:  Merger with [[generalized scale-free model]] 

message: It is strange that the article does not mention the generative model described in the PhD thesis of Lada Adamic circa 1999. Gritzko (talk) 15:54, 21 February 2013 (UTC)
thread_title:  Generative models 

message: I think the following paragraph from the section "Characteristics" should be rewritten 
Another important characteristic of scale-free networks is the clustering coefficient distribution, which decreases as the node degree increases. This distribution also follows a power law. This implies that the low-degree nodes belong to very dense sub-graphs and those sub-graphs are connected to each other through hubs. Consider a social network in which nodes are people and links are acquaintance relationships between people. It is easy to see that people tend to form communities, i.e., small groups in which everyone knows everyone (one can think of such community as a complete graph). In addition, the members of a community also have a few acquaintance relationships to people outside that community. Some people, however, are connected to a large number of communities (e.g., celebrities, politicians). Those people may be considered the hubs responsible for the small-world phenomenon.
The very first sentence in this para doesn't look correct to me. Certainly some real networks that seem to follow a power-law type of degree distribution and certain mathematical models of scale-free network do indeed have this trend for their local clustering coefficients but this is not generic feature of scale-free networks. For example, the Price model (as well as the Barabasi model) does not reproduce any such trend. Similarly, there exist real networks with power-law distributions for which this feature does not hold (especially those which are actually embedded in geographical space). 
Snehalshekatkar (talk) 15:09, 4 August 2016 (UTC)
thread_title:  Clustering coefficients' distribution in scale-free network 

message: The first sentence of this article:
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically, so that any part of the network has a similar structure to the whole
Really? Can I not have a network with a power-law degree distribution whose parts don't look like the whole network? A Trivial example is the one with a core-periphery structure. For now, I am removing this description. Please discuss if I have misunderstood it. 
Snehalshekatkar (talk) 11:46, 25 January 2017 (UTC)
thread_title:  Similar structure at all levels? 

message: Barabasi-Albert model has already been followed by a large number of variants and also many new models have been proposed which have been claimed to be giving rise to the scale-free structure. Such models certainly occupy important place in the study of networks. However, many such models have assumed many things about real networks and hence as the field maturates over time, the naive models tend to lose their importance since they don't add much to our knowledge. This implies that many recent models which claim to give rise to scale-free structure etc do not deserve mention in this article unless they are extra-ordinarily new and are well supported by empirical data providing a completely new knowledge. I have just now removed one such model and I request everyone to refrain adding more models without discussing them on the talk page. 
Snehalshekatkar (talk) 17:40, 3 February 2017 (UTC)
thread_title:  Stop adding more generative models for scale-free networks 

message: Is this grammatical,  semantics notwithstanding?
7 Novel characteristics	Edit
For a scale-free network with {\displaystyle n} n nodes and power-law exponent {\displaystyle \beta >3} {\displaystyle \beta >3}, the induced subgraph is constructed by vertices with degrees larger than {\displaystyle \log {n}\times \log ^{*}{n}} {\displaystyle \log {n}\times \log ^{*}{n}} is a scale-free network with {\displaystyle \beta '=2} {\displaystyle \beta '=2}, almost surely (a.s.).[42] ... Zezen (talk) 20:05, 15 November 2019 (UTC)
replies: text: If you remove the first "is", then its grammatical. Semantically, it seems plausible, it someone explained what the heck \log ^{*}{n} is supposed to mean. 67.198.37.16 (talk) 02:13, 25 February 2020 (UTC)
thread_title:  English please 

message: In the article, it has a template that says "This article needs attention from an expert in mathematics." It asks for a reason. I don't know how to add a reason to the template, but I'll give a reason here.
I don't think the article contains errors, but it is somewhat disordered and repetitive, especially in the second half. 
It should be edited by somewhat who knows the subject well enough to have confidence in what should be emphasized, and what should be rewritten.
2001:171B:2274:7C21:985E:DD36:E438:7F83 (talk) 14:55, 6 November 2021 (UTC)
thread_title:  This article needs attention from an expert in mathematics