Prsentation PowerPoint
IC 05 / semestre printemps 2008
IC 05 / semestre printemps 2008
Franck.ghitallaDpartement TSHPrsident de WebAtlas
[email protected]
IC 05 / semestre printemps 2008
Forme(s) et type(s) de rseaux (between order and randomness)
Agrgats et loi de puissance (information geography)
Dynamics (information IN and ON nets)
Corrlation structure/contenu (information distribution on
power-law topology)
Cadres conceptuelsA.-L. BARABASI linked - the new science of
networks, new ed. 2005.S. JONHSON -emergence: the connected lives
of ants, brains, cities, and software, 2002.
Thorie des graphesD. WATTS six degrees - the science of a
connected age, 2004.S. STROGATZ - sync: the emerging science of
spontaneous order, 2004.M. NEWMAN - the structure and dynamics of
networks, 2003.
Web-MiningS. CHAKRABARTI mining the web, 2002.J. KLEINBERG -
algorithm design, 2006.
InfoVizB. SHNEIDERMAN - readings in information visualization:
using vision to think, 1999.
Ouvrages de rfrence en Network SciencesIC 05 / semestre
printemps 2008
IC 05 / semestre printemps 2008
The problem : in social networks, web graphs or cells
organisation (and even each complex system), we have to understand
the presence of two contradictory properties.
On the one hand, the network should display a large culstering
coefficient, meaning that on average a persons friends are far more
likely to know each other than two people chosen at random. On the
other hand, it should be possible to connect two people chosen at
random via a chain of only a few intermediaries. (D; Watts, p77,
Six Degrees)
IC 05 / semestre printemps 2008
Most of networks (not only social networks) display what we call
clustering, which is really just to say that most peoples friends
are also to some extent friends of each other (D. Watts, p40, Six
Degrees)1) Clusters, proximity and long distances
IC 05 / semestre printemps 2008
Most of real networks (web, biology, social organization) are
highly clusteredDans un rseau social, si chaque agent a 100 amis,
et eux-mmes 100, etc...A 5 degrs de distance, on arrive 9
milliards. A priori, mathmatiquement, ce type d'expansion permet de
comprendre les fameux 6 degrees constants ( gauche).
Cependant, dans les rseaux sociaux ou sur le web pour les
sites/pages, il existe une forte redondance en termes de structure
: mes amis ont de grandes chances d'tre aussi les amis de mes amis
(disons, dans le mme cluster social ou communaut).
IC 05 / semestre printemps 2008
Graphe de sitesGraphe de mots-clef
IC 05 / semestre printemps 2008
La structure trs clusterise du web se mesure aisment partir de
calculs de densit pour la distribution de la connectivit hypertexte
entre sites. C'est l'un des principes dvelopps par J. Kleinberg ds
1996 pour la conception de l'algorithme HITS (Hypertext Induced
Topic Search).
IC 05 / semestre printemps 2008
Some of the properties of extremely complicated systems can be
understood without knowing anything about their detailed structure
or governing rules (D. Watts, p65, Six Degrees)2) Randomness,
universality and complex systems
IC 05 / semestre printemps 2008
A random graph is, as the name might suggest, a network of nodes
connected by links in a purely random fashion (D. Watts)
(gauche) Random Graphe (non-orient et orient)
(droite) Random Graph - (Rnyi)
IC 05 / semestre printemps 2008
All we needed to do was find a way to tune each network between
complete order and complete disorder in a way that it traced
through all the various intermediate stages (D. Watts, p86, Six
Degrees)3) Small World
IC 05 / semestre printemps 2008
Clustering Degree = HighDistance Degree = HighClustering Degree
= LowDistance Degree = LowClustering Degree = HighDistance Degree =
Low
IC 05 / semestre printemps 2008
A space of possible worlds the parameter we can tune from 0 to
1, from randomness to order in wich, at one end of the spectrum
individuals always make new friends through thier current friends
and, at the other end, they never do. in the middle, there is a
version of reality. (D. Watts).
The BetaModel,the order-randomness-spectrum(D. Watts, S.
Strogatz)
Orderfrom 0 to 1Randomnessfrom 0 to 1En moyenne, pour un network
de 1 million de nuds distribu en mode rgulier (avec pour chaque nud
100 voisins proches (50 gauche, 50 droite), la distribution de 5
liens en mode random fait chuter les distances moyennes de 50%. Il
faut multiplier ce chiffre par 10 (soit 5x10 = 50) pour faire
chuter la moyenne encore de 50 %. Et ainsi de suiteLes effets sont
donc dcroissants.
IC 05 / semestre printemps 2008
3 proprits des web-graphs a) de forme b) de distribution de
lordre c) de domaines(mots, liens, acteurs)
IC 05 / semestre printemps 2008
IC 05 / semestre printemps 2008
IC 05 / semestre printemps 2008
Franck.ghitallaDpartement TSHPrsident de WebAtlas
[email protected]
