Transcript leskovec.kdd06.305.p..

CMU SCS
??
??
KDD 2006
Leskovec & Faloutsos
1
CMU SCS
Sampling from Large Graphs
poster# 305
Jurij (Jure) Leskovec
Christos Faloutsos
Carnegie Mellon University
KDD 2006
Leskovec & Faloutsos
2
CMU SCS
Problems and recommendations
•
•
•
•
•
•
Q: How to sample from a large graph?
A: FF, RN
Q: Which properties to preserve?
A: (at least) the 13 ones we list
Q: How to measure success/similarity?
A: K-S, towards ‘back-in-time’ version
KDD 2006
Leskovec & Faloutsos
3
CMU SCS
Criteria
•
•
•
•
•
•
STATIC
in-degree; out-degree
distribution
distr. of WCC; SCC
hop-plot; hop-plot for WCC
distr. of first left singular vector
values
scree plot
distr. of clustering coefficient
KDD 2006
Leskovec & Faloutsos
•
•
•
•
TEMPORAL
Densification
power law
shrinking
diameter
normalized
size of largest
c.c.
first eigenvalue
4
CMU SCS
Targets
• scale-down (= fewer nodes; same diameter,
same degree etc)
• back-in-time (match an earlier, real, smaller
version of the graph)
KDD 2006
Leskovec & Faloutsos
5
CMU SCS
Sampling Methods
• RN random nodes
• RPN pageRank
random nodes
• RDN random
nodes, degreebiased
KDD 2006
• RE random
edges
• RNE
• HYB (Hybrid)
Leskovec & Faloutsos
• RNN
• RJ random
jump
• RW random
walk
• FF Forest fire
6
CMU SCS
4 Datasets
• Arxiv (author-paper)
• Citation (HEP-TH, HEP-PH)
• A.S.
• epinions.com
26K - 500K edges
KDD 2006
Leskovec & Faloutsos
7
CMU SCS
Diameter vs N;
KDD 2006
CC vs degree
Leskovec & Faloutsos
8
CMU SCS
degree distribution; avg CC vs N
KDD 2006
Leskovec & Faloutsos
9
CMU SCS
diameter
KDD 2006
DPL
Leskovec & Faloutsos
10
CMU SCS
D-statistic vs sample size
better
scale-down
KDD 2006
back-in-time
Leskovec & Faloutsos
11
CMU SCS
Conclusions
•
•
•
•
random nodes + a little exploration -> FF
(RN, RJ are close)
15% sample seems enough
back-in-time concept
KDD 2006
Leskovec & Faloutsos
12