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 Olga Klopp (CREST - UP10) Statistical Network Analysis 2 / 7
Yeast Protein-Protein Interaction Problem Find the hubs Olga Klopp (CREST - UP10) Statistical Network Analysis 3 / 7
Trophic Network Problem Find groups with strong connexions Olga Klopp (CREST - UP10) Statistical Network Analysis 4 / 7
Other structures... Determine motifs : Motifs = recurrent and statistically significant sub-graphs or patterns. Detection of anomalies (e.g. detection of hacking attacks ) ... Olga Klopp (CREST - UP10) Statistical Network Analysis 5 / 7
A null Model: Erd¨ os-R´ enyi Erd¨ os-R´ enyi random graph G ( n, p ) : ( A ij : i < j ) are i.i.d. Bernoulli ( p ) and A ii = 0 . Olga Klopp (CREST - UP10) Statistical Network Analysis 6 / 7
A null Model: Erd¨ os-R´ enyi Erd¨ os-R´ enyi random graph G ( n, p ) : ( A ij : i < j ) are i.i.d. Bernoulli ( p ) and A ii = 0 . Olga Klopp (CREST - UP10) Statistical Network Analysis 6 / 7
A null Model: Erd¨ os-R´ enyi Erd¨ os-R´ enyi random graph G ( n, p ) : ( A ij : i < j ) are i.i.d. Bernoulli ( p ) and A ii = 0 . Remark: deg ( i ) ∼ B in ( 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 heterogeneous structure clustering nodes that play the same role in the graph sparse Dolphine Social Network [Newman and Girvan(04)] Olga Klopp (CREST - UP10) Statistical Network Analysis 7 / 7
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