Sampling from Large Graphs poster

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Sampling from Large Graphsposter 305

• Jurij (Jure) Leskovec
• Christos Faloutsos
• Carnegie Mellon University

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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

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Criteria
STATIC
TEMPORAL

• 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

• Densification power law
• shrinking diameter
• normalized size of largest c.c.
• first eigenvalue

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Targets

• scale-down ( fewer nodes same diameter, same
  degree etc)
• back-in-time (match an earlier, real, smaller
  version of the graph)

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Sampling Methods

• RN random nodes
• RPN pageRank random nodes
• RDN random nodes, degree-biased

• RE random edges
• RNE
• HYB (Hybrid)

• RNN
• RJ random jump
• RW random walk
• FF Forest fire

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4 Datasets

• Arxiv (author-paper)
• Citation (HEP-TH, HEP-PH)
• A.S.
• epinions.com
• 26K - 500K edges

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Diameter vs N CC vs degree
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degree distribution avg CC vs N
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diameter
DPL
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D-statistic vs sample size
better
scale-down
back-in-time
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Conclusions

• random nodes a little exploration -gt FF
• (RN, RJ are close)
• 15 sample seems enough
• back-in-time concept