Statistical Network Analysis Olga Klopp MODALX, Universit e Paris - - PowerPoint PPT Presentation

Statistical Network Analysis

Olga Klopp

MODAL’X, Universit´ e Paris Nanterre - CREST, ENSAE

Olga Klopp (CREST - UP10) Statistical Network Analysis 1 / 7

Social Political Blog Network

Problem

Bisection of the graph

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Yeast Protein-Protein Interaction

Problem

Find the hubs

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Trophic Network

Problem

Find groups with strong connexions

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Other structures...

Determine motifs : Motifs = recurrent and statistically significant sub-graphs or patterns. Detection of anomalies (e.g. detection of hacking attacks ) ...

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A null Model: Erd¨

• s-R´

enyi

Erd¨

• s-R´

enyi random graph

G(n, p): (Aij : i < j) are i.i.d. Bernoulli(p) and Aii = 0.

Olga Klopp (CREST - UP10) Statistical Network Analysis 6 / 7

A null Model: Erd¨

• s-R´

enyi

Erd¨

• s-R´

enyi random graph

G(n, p): (Aij : i < j) are i.i.d. Bernoulli(p) and Aii = 0.

Olga Klopp (CREST - UP10) Statistical Network Analysis 6 / 7

A null Model: Erd¨

• s-R´

enyi

Erd¨

• s-R´

enyi random graph

G(n, p): (Aij : i < j) are i.i.d. Bernoulli(p) and Aii = 0. Remark: deg(i) ∼ Bin(n − 1, p). if p is constant, the mean degree is proportional to n (dense case) if p ≈ c/n, the mean degree is of constant order (sparse case)

Olga Klopp (CREST - UP10) Statistical Network Analysis 6 / 7

Real world networks

Dolphine Social Network [Newman and Girvan(04)]

heterogeneous structure clustering nodes that play the same role in the graph sparse

Olga Klopp (CREST - UP10) Statistical Network Analysis 7 / 7