Estrada index (migrated from Trac #605)

[networkx-trac]

Original ticket https://networkx.lanl.gov/trac/ticket/605
Reported 2011-07-22 by trac user franckkalala, assigned to @hagberg.

In chemical graph theory, the Estrada index is a topological index of protein folding. The index was first defined by Ernesto Estrada as a measure of the degree of folding of a protein,[1] which is represented as a path-graph weighted by the dihedral or torsional angles of the protein backbone. This index of degree of folding has found multiple applications in the study of protein functions and protein-ligand interactions.

[1] E. Estrada, Chem. Phys. Lett. 319, 713 (2000).

See also here http://en.wikipedia.org/wiki/Estrada_index

[networkx-trac]

Attachment in Trac by trac user franckkalala, 2011-07-25: eeindex.py

[networkx-trac]

Attachment in Trac by trac user franckkalala, 2011-07-25: test_eeindex.py

[networkx-trac]

Comment in Trac by trac user franckkalala, 2011-07-25

test for eeindex module;

eragon@eragon-laptop:~/sci$ nosetests -v test_eeindex.py
test_eeindex.TestEstradaIndex.test_estrada_index ... ok
test_eeindex.TestEstradaIndex.test_estrada_index_exp ... ok

---

Ran 2 tests in 0.134s

OK

[networkx-trac]

Comment in Trac by @hagberg, 2011-07-31

That looks good, thanks. I think this should be added in with the code in #501 since it is almost the same as communicability_centrality. Maybe we can use some of the same code, e.g. sum(communicability_centrality(G).values())?

[networkx-trac]

Comment in Trac by Aric Hagberg <aric.hagberg, 2011-07-31

In [214d0fe/networkx]:
'''
#!CommitTicketReference repository="networkx" revision="214d0fecb90c51daeb7a1663815d9653c3a412ec"
Add Estrada index.
Addresses #605
'''

[networkx-trac]

Comment in Trac by trac user franckkalala, 2011-07-31

That looks good, thanks. I think this should be added in with the code in #501 since it is almost the same as communicability_centrality. Maybe we can use some of the same code, e.g. sum(communicability_centrality(G).values())?

Yes is a good idea, thanks.

[networkx-trac]

Comment in Trac by @hagberg, 2011-09-16

[vlado-s]

Just a quick note - in Chem. Phys. Lett. 319 (2000) 713 (where Estrada index is introduced) it is defined as
I = sum over i of exp{lambda(i)}
Here lambda(i) are the eigenvalues of the adjacency matrix A of graph G.
However sometimes (e.g. in Bioinf. 18 (2002) 697 and apparently onward) he uses it normalised by N, which is the dimension of the adjacency matrix (number of nodes in G).
The value calculated by NetworkX is the first value (not normalised) - just in case someone was wondering why the large number :)
Also, obviously, NetworkX does not put any weights on the diagonal of A - as used (recommended) in chemical application.