# Talk:Erdős–Rényi model

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According to: They do not account for the formation of hubs. Formally, the degree distribution of ER graphs converges to a Poisson distribution, rather than a power law observed in most real-world, scale-free networks. http://en.wikipedia.org/wiki/Watts_and_Strogatz_model#Rationale_for_the_model

And in the main article it says: "Properties of G(n, p)

As mentioned above, a graph in G(n, p) has on average \tbinom{n}{2} p edges. The distribution of the degree of any particular vertex is binomial:"

Am I right to assume that it is the G(n, M) model which has a poisson distribution or did I miss something or is there a mistake. As a general comment the main article seems to focus mainly on the G(n, M) model with little discussion on the G(n, p) model.

S243a (talk) 21:45, 4 July 2009 (UTC)John Creighton

After some thought it seems to be the case that if there are at least 10 times as many nodes as the average order then the Poisson distribution is a suitable approximation even though the underlying statistics are binomial. Given that in most areas of social science the number of nodes is large in comparison to the order then Poisson statistics usually are appropriate.

S243a (talk) 00:54, 5 July 2009 (UTC)John Creighton

## Abbreviations

I find this just a little bit too much: "Magyar Tud. Akad. Mat. Kutató Int. Közl." Can anyone tell me what that stands for? Abbreviations in references made sense when paper was expensive. But do abbreviations to the point of impossible-to-understand really belong in Wikipedia?

To answer my own question, I had some luck finding the paper on this page http://www.renyi.hu/~p_erdos/Erdos.html (#1960-10). The expansion of the abbreviated text appears to be "A Matematikai Kutat\'{o} Int\'{e}zet K\"{o}lem\'{e}nyei" (as according to http://www.citeulike.org/user/muraken/article/4012385), and in English that seems to be translated (and abbreviated!) as "Publ. Math. Inst. Hungar. Acad. Sci" (as according to http://www.citeulike.org/group/3072/article/1666220 and http://mathworld.wolfram.com/RandomGraph.html).

## Spectrum?

Article enhancement request: what is the spectrum of these graphs? How does it compare to that of scale-free graphs? linas (talk) 18:47, 24 March 2010 (UTC)

Hi Linas, You may be interested in this: http://arxiv.org/abs/cond-mat/0102335 --fij (talk) 13:58, 13 July 2010 (UTC)

## asymptotically almost surely

I think would be better to substitute "almost surely" with "asymptotically almost surely" as here.--Natematic (talk) 19:54, 7 October 2012 (UTC)

## Interacting Erdős–Rényi random graphs model

The author decided to distinguish matrices from matrix elements by boldfacing. This is not documented in wp:MSM; I find this convention confusing so I edited the descriptions to be more explicit (while keeping the original style). --Yecril (talk) 15:03, 2 March 2014 (UTC)