Edinburgh Napier University

  Previous studies have shown that there is an intricate relationship between the topology of an idiotypic network and its resulting properties. However, empirical studies can only be performed by pre-selecting both a shape-space and affinity function. This introduces a number of simplifications into any model and makes it subsequently difficult to abstract the underlying contribution made by the topology from the particular instantiation of the model. In this paper, we introduce the concept of the potential network as a method in which abstract network topologies can be directly studied which allows us to bypass any definition of shape-space and affinity function. By using ideas from complex network theory to study a variety of homogeneous and heterogeneous potential networks, we show that bi-partide and heterogeneous topologies are able to tolerate antigens in certain regions, where as those showing high levels of clustering are unable to do so. It is also shown that the equilibrium topology resulting from traditional immune dynamics depends dramatically on the potential topology of a network.