8
L 25 - Communities + Influent in Graphs . tip G. ' d. E) g vz social network . uz Vs people ( ententes ) vc . E = connections

Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

L 25 - Communities

+ Influent in Graphs.

tip G.' d. E)

gvz

social network

. uzVs people ( ententes)

vc.

E = connections

Page 2: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

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 .

Page 3: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

Why Do People Join Groups ?

÷friends in group

broaderY@ ts to

[email protected].

support #€.

. clique

Groupis

Mdrf

persuasive

Page 4: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

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?

Page 5: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

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

[email protected]

monitdes

Page 6: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

Communities are . not partitions

→ tightly connected subset of graph .

→ can overlap

→set does not need to portvtvon Un

Page 7: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

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

Page 8: Influentjeffp/teaching/cs5140-S18/cs... · 2018. 12. 30. · Large Graphs µl= I billion (facebook) r f-rlfer \/ general( g (for ruble) notfully available ÷iolasg + usoaka-drawyears210

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