Re: size and network value

On 1 Jul 2010, at 01:17, Harry Halpin wrote:

> On Wed, Jun 30, 2010 at 6:11 PM, Henry Story <henry.story@gmail.com> wrote:
>> Just a thought following todays talk.
>> 
>> Why not get some networg graph experts to help us work out what the value of a global
>> social web would be? There is a lot of research in the field of network theory, and there
>> may be some interesting insights to be had from those areas.
> 
> I agree - you think there would be someone who can judge information
> "liquidity" as Tim Anglade put it and imagine some bright economicst
> could figure it out.

I am perhaps also thinking more of some calculations that would give us the size of 
the space available now, and a comparison with the space available to a global
Social Web. 

This is what Metcalf's law was attempting to do for the telecommunications network 
http://en.wikipedia.org/wiki/Metcalf's_law

What it really gives you is the potential of the network given the size of a 
*telephone* network. How many people can be put in communication. 

It is a bit like discovering America. You want to know the size of the territory.
It must have helped:

  - to know america existed
  - that it was a lot bigger than Europe

I can imagine that it did not require a lot more argument than that to get 
explorers interested. Why? There was nothing there, only a lot of unknown,
and danger. But it is the potential that was so interesting...

So on metcalf's law let us look at the value of:

 France:   65 million^2 = 4225000000000000 potential connections
 Germany:  81 million^2 = 6561000000000000 potential connections
 
 France&
 Germany: 146 million^2= 21316000000000000 potential connections

so the PotConn of the combined france+germany network is double
that of the sum of each.

What is the value for a country the size of France to join the global
telecommunication network?

 World:  6 billion^2 = 36000000000000000000 Pot conn
 World/France = 8520

So even though France is 1/100 of the world population, by playing in a global
network it is suddenly part of a network that is 8520 times bigger.
 
Now metcalf's law is based on one type of connection. Call it 

tel:canCall a owl:Property, owl:SymmetricProperty;
   rdfs:comment "a relation relating two people who can call each other";
   owl:domain foaf:Person;
   owl:range foaf:Person .

Iin the social networking space there are potentially a lot more relations than
this one. So what are the maths then? 

For example if we are concerned about the number of groups that we can be part of
then this follows the power law. The size of the power set of 1000 people, ie the
number of different groups that can be made with its members is

2^1000 =
10715086071862673209484250490600018105614048117055336074437503883703\
51051124936122493198378815695858127594672917553146825187145285692314\
04359845775746985748039345677748242309854210746050623711418779541821\
53046474983581941267398767559165543946077062914571196477686542167660\
429831652624386837205668069376

for 10 thousand it is 

2^10000 =
19950631168807583848837421626835850838234968318861924548520089498529\
43883022194663191996168403619459789933112942320912427155649134941378\
11175937859320963239578557300467937945267652465512660598955205500869\
18193311542508608460618104685509074866089624888090489894838009253941\
63325785062156830947390255691238806522509664387444104675987162698545\
32228685381616943157756296407628368807607322285350916414761839563814\
58969463899410840960536267821064621427333394036525565649530603142680\
23496940033593431665145929777327966577560617258203140799419817960737\
82456837622800373028854872519008344645814546505579296014148339216157\
34588139257095379769119277800826957735674444123062018757836325502728\
32378927071037380286639303142813324140162419567169057406141965434232\
46388012488561473052074319922596117962501309928602417083408076059323\
20161268492288496255841312844061536738951487114256315111089745514203\
31382020293164095759646475601040584584156607204496286701651506192063\
10041864222759086709005746064178569519114560550682512504060075198422\
61898059237118054444788072906395242548339221982707404473162376760846\
61303377870603980341319713349365462270056316993745550824178097281098\
32913144035718775247685098572769379264332215993998768866608083688378\
38027643282775172273657572744784112294389733810861607423253291974813\
12019760417828196569747589816453125843413595986278413012818540628347\
66490886905210475808826158239619857701224070443305830758690393196046\
03404973156583208672105913300903752823415539745394397715257455290510\
21231094732161075347482574077527398634829849834075693795564663862187\
45694992790165721037013644331358172143117913982229838458473344402709\
64182851005072927748364550578634501100852987812389473928699540834346\
15880704395911898581514577917714361969872813145948378320208147498217\
18580113890712282509058268174362205774759214176537156877256149045829\
04992461028630081535583308130101987675856234343538955409175623400844\
88752616264356864883351946372037729324009445624692325435040067802727\
38377553764067268986362410374914109667185570507590981002467898801782\
71925953381282421954028302759408448955014676668389697996886241636313\
37639390337345580140763674187771105538422573949911018646821969658165\
14851304942223699477147630691554682176828762003627772577237813653316\
11196811280792669481887201298643660768551639860534602297871557517947\
38524636944692308789426594821700805112032236549628816903573912136833\
83935917564187338505109702716139154395909915981546544173363116569360\
31122249937969999226781732358023111862644575299135758175008199839236\
28461524988108896023224436217377161808635701546848405862232979285387\
56234865564405369626220189635710288123615675125433383032700290976686\
50568557157505516727518899194129711337690149916181315171544007728650\
57318955745092033018530484711381831540732405331903846208403642176370\
39115506397890007428536721962809034779745333204683687958685802379522\
18629120080742819551317948157624448298518461509704888027274721574688\
13159475040973211508049819045580341682694978714131606321068639151168\
1774304792596709376

As you can see this number grows exceedingly fast.

> 
> Of course, this would have to be balanced by privacy concerns, and one
> can imagine genuine privacy on the Social Web would reduce information
> liquidity...but in other regards, a decentralized network that let
> people chose to open their data would rapidly increase information
> liquidity of certain kinds.
> 
> There has been some economic work in the area - Yochai Benkler comes
> to mind - but to my knowledge, nothing addressing distributed social
> networks per se.
> 
>> 
>>        Henry
>> 
>

Received on Thursday, 1 July 2010 08:18:07 UTC