Biomedical Engineering Reference
In-Depth Information
Figure 3. (a) The random network model is constructed by laying down
N
nodes and connecting
each pair of nodes with probability
p
. The figure shows a particular realization of such a network
for
N
= 10 and
p
= 0.2. (b) The scale-free model assumes that the network constantly grows by
the addition of new nodes. The figure depicts the network at time
t
(nodes connected by green
links) and after addition of a new node at time
t
+ 1 (red links). With the introduction of new
nodes, already highly connected ones are more favored to be connected to the new one than less
connected ones. This procedure is called
preferential attachment
. (c) The iterative construction
of a hierarchical network starts from a fully connected cluster of four nodes (blue), which is
replicated three times. Subsequently, the peripheral nodes of each replica (green) are connected
to the central node of the original module. Repeating replication and the connection step with the
16-node module (red) leads to a 64-node network that provides scale-free topology and is built
by nested modules. (d) The random network is rather homogeneous, i.e., most nodes have about
the same number of links. (e) In contrast, a scale-free network is extremely inhomogeneous:
while the majority of nodes have one or two links, a few nodes have a large number of links,
preserving system integrity. To show this, five nodes with the highest number of links are col-
ored red and their first neighbors green. While in the random network only 27% of the nodes are
reached by the five most-connected nodes, in the scale-free network more than 60% are, demon-
strating the key role hubs play in a scale-free network. Note that both networks contain the same
number of nodes and links. (f) A hierarchical network still preserves a scale-free organization
and displays the inherent modularity of nodes. The node's affiliation with a certain module is
indicated by different colors. However, the underlying network structure clearly indicates
blurred boundaries of its modules.
node with
m
links is added to the network, connecting to a previously present
node
i
with probability
k
1
=
,
i
[5]
i
k
j
j
