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a high robustness against random node removal [67]. In biological networks this
might correspond to the random deletion (or loss of function) of a gene, so that all
edges passing through it are interrupted. In the case of regulatory networks, the
disappearance of a TF determines the loss of its control over the target genes. On
the contrary, scale-free networks are highly sensitive to directed attack, i.e. removal
of hubs, a strategy that can be exploited in drug design.
In a regulatory network the outdegree corresponds to the number of genes a
given transcription factor is able to regulate, so that TFs with high degree can be
thought as the master regulators; on the converse, the indegree of a gene corresponds
to the complexity of its regulation.
The properties of hub proteins are of particular interest, not least because, being
involved in a number of cellular processes, they are attracting candidates for antimi-
crobial agents. Studying protein-protein interaction networks, it has been claimed
that hubs might be physiologically more important (i.e., less dispensable) [76{79]
and slow evolving [80{83]. Not all analysis, however, support this idea probably
because of biased and less-than reliable global PPI data; for this reason Batada
et al. [84] studied a comprehensive literature-curated dataset of well-substantiated
protein interactions in Saccharomyces cerevisiae nding a relatively robust correla-
tion between degree and dispensability (i.e. highly connected nodes are more often
essential). In contrast, no correlation with evolutionary rates has been found.
Average Shortest Path Length, ASPL: Path length tells us how many links
we need to pass through to travel between two nodes and it is used as a measure
of distance in graphs. The paths connecting two nodes can be many, so that it is
common practice to use the shortest path. ASPL is the average over all shortest
paths in the network giving a measure of networks' navigability.
In a recent work the dynamics of a biological network on a genomic scale have
been addressed [85] by integrating transcriptional regulatory information and gene-
expression data for multiple conditions in Saccharomyces cerevisiae. We will illus-
trate the results of that work and the interpretation given by the authors. The net-
works reconstructed from dierent conditions have large topological dierences: reg-
ulatory interactions conserved in dierent conditions mostly regulate house-keeping
functions and, while a few TFs are always highly connected, most of them becomes
active only in a few cases. Luscombe and collaborators [85] identify ve condition-
specic sub-networks which they further classify into endogenous, e.g. cell cycle
and sporulation responding to an internal programme, and exogenous, e.g. diauxic
shift, DNA damage and stress response, controlled by extracellular signals. The dif-
ferences between the two classes of sub-networks can be summarized in four main
points:
(1) the average in-degree decreases by 20% from endogenous to exogenous condi-
tions indicating that TFs are going to regulate genes in simpler combinations;
