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L 25 - Communities
+ Influent in Graphs.
tip G.' d. E)
gvz
social network
. uzVs people ( ententes)
vc.
E = connections
Large Graphs
µl= I billion ( facebook)r f- rlfer
¥\/ general (g ( for ruble ) not•
.
fully available.
÷iolasg + usoaka- draw
210years ago Karate Club\5
-
- Bo nodes + small.in#dlshEf.eNot Erdins . Reusi Model
www.d#niP)=ena.hIogddgeesC, ;) exist up , P .
Why Do People Join Groups ?
÷friends in group
broaderY@ ts to
IeaIaYt@Gsgoy.e.
support #€.
. clique
Groupis
Mdrf
persuasive
Preferential- new edges
,more likely to
form trianglesthan random
.
notErda 's
'
- Ren,yi
aiif node i has new!D•k
aCommon
few triangles if toofjhe . afriend↳ nose libels too many wrangles.depressed
is Bot?
Between ness Hishbetu score
@p*I*O¥E.EE#E*i@se:e:
Betel A. B) = fraction of shortest paths- that use aedse AiB)
all pairs of V.,
u,
e- µ
Howimpotant_iedseAf.B@QEftwCandefvaeBetwCvicIneReFeYIwcYfmp.com
monitdes
Communities are . not partitions
→ tightly connected subset of graph .
→ can overlap
→set does not need to portvtvon Un
tkodulatg defined on subset Cold.
Q( c) =(fraction edges ink ) - ftp.gtg.gg,↳)⇒ElectingEE.EE 's. Adjacency matrix Ai ;=l ifedse
C) d-W ,
. Expected matrix Eg. =di#ZIEI
yI*f di = degree Vi = # eases whichinclude Ud
d⇐5g(D=.it#f4e.&.cCAiiy*iiDregularize
windGfuie )
most subset SCV
when ill vi. V;ES have
M$ edge ( vi. up c- E
a. ftp.go.wsAprrori Aig .
�1� Find all edges in G
@ such either,
to check it triangle
�3� seach Pg to ii. is 4 - diqce
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