
246 Feedback Control in Systems Biology
where
p
(k)
j
=
K
(k)
j
n
P
l=1
K
(k)
l
(7.46)
is the probability of inserting a new edge starting from node j and K
(k)
l
is the number of outgoing connections from the l-th node at the k-th
iteration. The µ(k) edges with the largest scores in
˜
G
(k)
are selected
and added to the network; µ(·) is chosen as a decreasing function of k,
that is µ(k) = ⌈n/k⌉. T hus, the network grows rapidly at the begin-
ning and is subsequently refined by adding smaller numbers of nodes at
each iteration. The form of the function p(·) stems from the so-called
preferential attachment (PA) mechanism, which states that in a growing
network new edges