  Some years ago a cellular automata model was proposed to describe the
evolution of the immune repertoire of B cells and antibodies based on Jerne's
immune network theory and shape-space formalism. Here we investigate if the
networks generated by this model in the different regimes can be classified as
complex networks. We have found that in the chaotic regime the network has
random characteristics with large, constant values of clustering coefficients,
while in the ordered phase, the degree distribution of the network is
exponential and the clustering coefficient exhibits power law behavior. In the
transition region we observed a mixed behavior (random-like and exponential) of
the degree distribution as opposed to the scale-free behavior reported for
other biological networks. Randomness and low connectivity in the active sites
allow for rapid changes in the connectivity distribution of the immune network
in order to include and/or discard information and generate a dynamic memory.
However it is the availability of the low concentration nodes to change rapidly
without driving the system to pathological states that allow the generation of
dynamic memory and consequently a reproduction of immune system behavior in
mice. Although the overall behavior of degree correlation is positive, there is
an interplay between assortative and disassortative mixing in the stable and
transition regions regulated by a threshold value of the node degree, which
achieves a maximum value on the transition region and becomes totally
assortative in the chaotic regime.
