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In-Depth Information
Table 2.2.
The parameter inferred for several types of networks. PI: Protein Interaction.
Network Type
Reference
Yeast paralogs PI divergence (n=274)
1.38
[68]
Yeast PI (data from [69])
2.80
[70]
Yeast PI (core data from [71])
2.2
[72]
C. elegans PI (data from [73])
1.8
[74]
Metabolic network E. nidulans
2.2
[72]
Protein domains family size (T. maritima)
3
[75]
Protein domains family size (C. elegans)
1.9
[75]
Homology of Plasmid encoded proteins ({proteobacteria; n = 3393)
1.32
[37]
Global Homologies of Nitrogen xation proteins (n = 4299)
2.3
[37]
and edge values reecting the degree of similarity between two sequences. The
following step is the clustering of the network, that can be done using one of the
algorithms cited above. Following the clustering procedure it is possible to analyze
the global topological properties of the network or to use data mining procedures
to characterize the function(s) of proteins of each cluster.
2.6. Statistical Properties of Biological Networks
Here we discuss the biological signicance of complex network concepts.
Degree: The degree or connectivity (k) of a node in its simplest form is the
number of links starting or reaching it. In directed graphs we can dene an incom-
ing degree (k
in
), i.e. the links received by a node, and an outgoing degree (k
out
)
summarizing the number of links sent by the node. In a regulatory network, the
indegree concerns regulated genes, while the outdegree concerns only TFs. The de-
gree distribution (P (k)) gives the probability that a node has k links. It is obtained
by counting the number of nodes with a certain number of links and dividing by
the total number of connected nodes. The degree distribution of most biological
networks ts a power-law (i.e. P (k)'k
, with '2) indicating the presence of
rare very connected nodes (hubs) [66] in a vast majority of nodes with only a few
connections. The value of determines many properties of the network; if it is very
small, the network's topology is highly dependent on the role of the hubs, whereas
for > 3 highly connected nodes are not relevant; in this case the network's behav-
ior approaches the random type. For 2 < < 3 there is a hierarchy of hubs, with
the most connected being in contact with a small fraction of all nodes; for = 2 a
hub-and-spoke network emerges, with the largest hub contacting a large fraction of
nodes (the so-called giant component).
In general, the unusual properties of scale-free networks are valid only for < 3
when the dispersion of the degree distribution (
2
=hk
2
ihki
2
) diverges as the
number of nodes increases; this results in a series of unexpected features, such as
