Re: [igraph] correlation between degree of a node and average degree of its neighbors

[Simone Gabbriellini]

Dear Jordi,

thanks for sharing your thoughts, but according to Latapy et al., Social 
Networks, 30 (2008) 31-48, the correlation has a pretty interesting 
interpretation, which does not rely on normalization. The actors-movies network 
data they show is an interesting example.

thanks,
Simone

Il giorno 25/nov/2010, alle ore 12.42, jordi torrents ha scritto:

> Hello,
> 
> 2010/11/24 Simone Gabbriellini <address@hidden>:
>> thanks,
>> 
>> that function is really it... but I am wondering if it works in a bipartite 
>> case... it should, right?
> 
> You have to be careful in order to make sense of the correlation
> between node degree and average degree of its neighbors in a bipartite
> network. Notice that since there are two sets of nodes and edges only
> can link nodes of different sets, if there is a big difference between
> the number of nodes of the two sets, the correlation will be biased
> because the set that contains less nodes will have higher degrees on
> average.
> 
> One possible approach would be to normalize the degree before running
> the correlation. In order to do that in a bipartite network, you will
> have to apply two separate normalizations for each node set:
> 
> nd_i = d_i / n_2 for i in V_1
> 
> nd_j = d_j / n_1 for j in V_2
> 
> where nd_i is the normalized degree for node i (which belongs to node
> set V_1), d_i is the raw degree of that node and n_2 is the number of
> nodes of node set V_2 (which is the maximum degree that a node of set
> V_1 could have).
> 
> Hope that helps.
> Salut!
> 
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