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Analysis of a Growth Model for Idiotypic
Networks
Emma Hart
School of Computing, Napier University
e.hart@napier.ac.uk
Abstract.
This paper presents an analysis of the global physical proper-
ties of an idiotypic network, using a growth model with complete dynam-
ics. Detailed studies of the properties of idiotypic networks are valuable
as one the one hand they offer a potential explanation for immunolog-
ical memory, and on the other have been used by engineers in applica-
tion of AIS to a range of diverse applications. The properties of both
homogeneous and heterogeneous networks resulting from the model in
an integer-valued shape-space are analysed and compared. In addition,
the results are contrasted to those obtained using other generic growth
models found in the literature which have been proposed to explain the
structure and growth of biological networks, and also make a useful ad-
dition to previous published results obtained in alternative shape-spaces.
We find a number of both similarities and differences with other growth
models that are worthy of further study.
1
Introduction
The study of the structure and growth of biological networks (e.g idiotypic net-
works or protein-protein interaction networks) has received much attention from
various disciplines in the past, for example statistical physics, mathematics and
immunology, as it becomes apparent that understanding the architecture and
construction process by which these networks are formed plays a crucial role in
understanding the dynamics that can then take place on such networks. Studies
in all these areas have led to the observation that biological networks are not
structured randomly. Frequently, a topology is observed in which there are a few
nodes which interact with a large number of other nodes (known as the
hubs
),
and many nodes which interact with only a few nodes. The same type of topology
is also observed in other real-world networks, such as social and technological
networks, for example co-authorship of physics papers or the world-wide-web —
such networks are referred to as scale-free, and the networks exhibit a number
of interesting properties when compared to random graphs of equivalent size.
A number of growth models have been proposed in an attempt to describe
the origins of these real-world networks. Perhaps the most prevalent is due to
Barabasi and Albert [1] which proposes a growth model based on preferential
attachment of new nodes to existing nodes with high degree, which results in a
network with scale-free properties. Whilst this model makes sense in the case of
