Wt: investigate a model where idiotypes (characterizing B lymphocytes and a
ntibodies of an immune system) and anti-idiotypes are represented by comple
mentary bit strings of a given length d allowing for a number of mismatches
(matching rules). In this model, the vertices of the hypercube in dimensio
n d represent the potential repertoire of idiotypes. A random set of (with
probability p,) occupied vertices corresponds to the expressed repertoire o
f idiotypes at a given moment. Vertices of this set linked by the above mat
ching rules build random clusters. We give a structural and statistical cha
racterization of these clusters, or in other words of the architecture of t
he idiotypic network. Increasing the probability p one finds at a critical
p a percolation transition where for the first time a large connected graph
occurs with probability 1. Increasing p further, there is a second transit
ion above Which the repertoire is complete in the sense that any newly intr
oduced idiotype rinds a complementary anti-idiotype. We introduce structura
l characteristics such as the mass distribution and the fragmentation rate
for random clusters, and determine the scaling behavior of the cluster size
distribution near the percolation transition. including finite size correc
tions. We find that slightly above the percolation transition the large con
nected cluster (the central part of the idiotypic network) consists typical
ly of one highly connected part and a number of weakly connected constituen
ts and coexists with a number of small, isolated clusters. This is in accor
dance with the picture of a central and a peripheral part of the idiotypic
network and gives some support to idealized architectures of the central pa
rt used in recent dynamical mean field models.