Robustness across the Structure of Sub-Networks: The Contrast between Infection and Information Dynamics

In this paper we make a simple theoretical point using a practical issue as an example. The simple theoretical point is that robustness is not 'all or nothing': in asking whether a system is robust one has to ask 'robust with respect to what property?' and 'robust over what set of changes in the system?' The practical issue used to illustrate the point is an examination of degrees of linkage between sub-networks and a pointed contrast in robustness and fragility between the dynamics of (1) contact infection and (2) information transfer or belief change. Time to infection across linked sub-networks, it turns out, is fairly robust with regard to the degree of linkage between them. Time to infection is fragile and sensitive, however, with regard to the type of sub-network involved: total, ring, small world, random, or scale-free. Aspects of robustness and fragility are reversed where it is belief updating with reinforcement rather than infection that is at issue. In information dynamics, the pattern of time to consensus is robust across changes in network type but remarkably fragile with respect to degree of linkage between sub-networks. These results have important implications for public health interventions in realistic social networks, particularly with an eye to ethnic and socio-economic sub-communities, and in social networks with sub-communities changing in structure or linkage.