Analysis of Regulatory and Interaction Networks from Clusters of Co-expressed Genes - Clustering Challenges in Biological Network - page 72

and stabilize the change in diameter in the presence of random failures. As a result
the network exhibits strong tolerance. However, targeted attacks have detrimental
effects on the network. Therefore, the presence of hubs (highly connected nodes)
is both an advantage, leading to robust networks, as well prone to complete failure
should a critical hub be affected.
We simulated random failures and attacks by analyzing the protein interaction
networks constructed based on the burn induced inflammatory response, as well as
an equivalent Erd os-Renyi [13] random network with the same number of nodes,
number of total links and average number of links per node. Specifically, the
gene interaction network: 146 nodes, 268 connections, and the average number
of connections per node was 3.67, whereas the Erd os-Renyi network: 146 nodes,
273 connections, and the average number of connections per node was 3.74. The
results are depicted on Fig. 3.11. It must be realized that although many other
studies analyze arbitrary networks with thousands of proteins, we concentrate on
a much smaller and sensitive network which is composed of proteins very rele-
vant to the inflammatory response resulting from severe burn injuries. However,
all the important characteristics of the expected responses were recovered, which
adds significant insight to the nature and structure of the generated framework. In
terms of our analysis we define failure as the random elimination of a node for
the network, whereas attack refers to a target removal of a specific (set) of nodes.
Therefore, failures are being presented as the average of numerous (500) simula-
tions of random eliminations of combinations of nodes from the networks. The
failure results indicate the average of multiple runs. In attack, we target nodes
based on their degree of connectivity, starting from the most highly connected
nodes. The inherent computational property of the network that we evaluate is the
average diameter of the network, which is quantified by evaluating the average
shortest path length in the network. This metric assess the change in the effective-
ness in communicating disturbances across the network. We therefore evaluate
the structural properties of the network in propagating disturbances and the impli-
cations of such disturbances in the effective properties of the network. Our goal is
to assess the fundamental differences between the two types of network, namely,
scale free and random.
Based on our simulation results we observed that random (ER) networks do
demonstrate very interesting characteristics. Because the distribution of connec-
tions is random, the response to random failures as well as attacks results in sim-
ilar changes on the average shortest path. This is a critical property that has been
previously well studied and established in ER-type of networks [44]. The devia-
tions from the theoretical curves are mostly due to the fact that unlike simulated
networks with thousands of nodes and connections, our ER network emulates the