Pagerank of Hippie genes

Question

[shivangi.agarwal800]

Hi

I want to calculate pagerank of all genes in Hippie network. Which tool would serve the purpose? Thanks in advance.

[h.mon]

Please add some more detail to your question. But provided your data follows the proper format, you can use pagerank from NetworkX.

[Jean-Karim Heriche]

Function page_rank() in the igraph R package.

[shivangi.agarwal800]

Thanks, I have calculated pagerank from igraph. It is fine, but when I am calculating eigen vector from igraph and comparing to the one calculated by centibin, I am getting different values, eg. My_Network_Edge_file

v1,v2
1,2
1,3
1,4
2,5
2,3
2,4
3,6
3,4
6,4
4,7

vertex as:

"1" "2" "3" "6" "4" "5" "7"

degree.cent$res(fine)

3 4 4 2 5 1 1

pagerank (fine)

1          2          3          6          4          5          7 
0.14446947 0.19732697 0.18885024 0.10253749 0.24104847 0.06336055 0.06240681

Eigen_centrality

1         2         3         6         4         5         7 
0.8097211 0.8658518 0.9351728 0.5594204 1.0000000 0.2503007 0.2890803

while eigenvector centrality from centibin was obtained as:

1         2        3        4         5         6         7
0.4187492 0.447773 0.4836268 0.5171524 0.1294436 0.2893056 0.1494986

More, I note that the values obtained from igraph when multiplied by 1.933666 will give exactly same value as by centibin.

What may be the reason?..

Please suggest..

Regards

[Ram]

Please use the formatting bar (especially the code option) to present your post better. I've done it for you this time.

[Jean-Karim Heriche]

By definition, you can scale an eigenvector and it will still be an eigenvector or put another way, the scale of an eigenvector is irrelevant. Many software will normalize eigenvectors to unit length.

[shivangi.agarwal800]

Can you please elaborate some more?

[Jean-Karim Heriche]

Given a square matrix A, λ and v are a number and vector respectively that satisfy the equation Av=λv. λ is called an eigenvalue and v is an eigenvector of A corresponding to the eigenvalue λ. You can see from the equation that multiplying v by a constant wouldn't change anything. This is basic linear algebra. Given how pervasive linear algebra is in science, I would encourage you to pick up a textbook on the subject.

[shivangi.agarwal800]

Thanks a lot for your explanation

[shivangi.agarwal800]

In addition, I want to know how to judge the importance of network nodes using centrality measures like degree, DMNC, MNC, MCC, EPC, bottleneck, eccentricity, closeness, radiality, betweenness, stress, clustering coefficient, pagerank..

Means that as we know the value of degree centrality is directly proportional to importance of node, the higher the degree, the more important is the node, likewise I want to know the relationship of other centrality scores with the importance of nodes. Are there values directly or inversely proportional to the importance of nodes? Is there any link addressing the same?.

Your suggestion is highly appreciated.

[Jean-Karim Heriche]

The wikipedia article on centrality explains many centrality measures. However, you should ask yourself what kind of biological information you're trying to get at and in this context what node importance is (and whether it is relevant). Given that most biological networks are incomplete, many of the numbers extracted from these graphs such as centrality measures have questionable generalization value. Consider the high degree of historical cancer genes (e.g. SRC, TP53 ...) and of ubiquitin in protein interaction graphs. The degrees of cancer genes has more to do with publication bias (you get more funding if you can link your favorite gene to a cancer gene and these have been studied far more and for a longer time than e.g. C3orf67) than with biology but the high degree of ubiquitin simply reflects that it is a covalent modification of many proteins and although it is biologically relevant, I wouldn't count this as the same type of protein interaction as what we're usually trying to describe in protein-protein interaction graphs.