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

[jordi torrents]

Simone,

Now I understand. I thought that you wanted to plot the degree
correlation for all nodes in both sets as it is usually done in
unipartite networks. Indeed if you plot separately the degree
correlation for each node set and compare it with their random
counterpart, following Latapy et al. (2008), you can do interesting
interpretations without worrying about degree normalization.

Salut!

2010/11/25 Simone Gabbriellini <address@hidden>:
> 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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