Whats curical for hypothesis testing on networks
having a good generative model for the network I want to test
Random graphs are not a good baseline (Erdös-Renyi)
Are summary statistics sufficient to compare networks
No, other characteristics are needed
Modularity and comunity structure detection
Whats a module ?
Any node set where I have
maximize inner module connections
low conenctions to other modules
NP hard
Maximize the following equation
Give an example where strict modularity fails ?
Social Ego networks
Clusters can overlap
e.g People can be part of Summer internship and a squash group
Name some centrality measures ?
Degree centrality
Closeness centrality ( distance to all other nodes)
Betweenness centrality (how important is a node to most shorteset paths)
How to compare grapths with each other
compute sufficient summary statistics
defince distance/similarity on theses statistics
use the distance matrix to generate a low dimensional embedding
Graphlet correlation distance
count how often a node appears in each feature
generate feature correlations
Whats the attack robistness of a network ?
estimate the influence of sequential OTU removal
the size of the largest connected component (not very robust if large)
natrual connectivity
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