The Architecture of Connectivity: A Key to Network Vulnerability, Complexity and Resilience.

This paper highlights the relevance of connectivity and its architecture as a general conceptual framework which underlies and integrates the concepts of network vulnerability, complexity, and resilience. In particular, it will be pointed out that connectivity architecture can be considered an explicit key element for network vulnerability and shock propagation. While the relevance of the various connectivity configurations is not clearly emphasised in the dynamic complexity models of the space-economy, it appears to play a primary role in network analysis. In this regard, the emerging recognition of connectivity architecture in relation to hubs ‒ and hierarchies of hubs ‒ in a complex network will help the enhancement of network resilience. The paper develops as follows. First, the notion of network vulnerability, which refers not only to the phenomenon of shocks, but also to the propagation of shocks in a network, will be examined. Here it appears that modelling vulnerability and shock propagation, also jointly with cascading disaster models, is strongly based on connectivity issues. The question is: How can conventional (complex) system dynamic modelling, as well as network modelling, take into account these shocks and connectivity dynamics from the methodological viewpoint? A review in this respect shows how connectivity is a 'hidden' element in these complexity models, for example, in chaos or (dynamic) competition models, where interaction parameter values might lead to vulnerable domains and chaotic behaviour. On the contrary, connectivity and its various topologies have a distinct, primary role in network analysis. The issue of network resilience appears therefore to be the 'response' to vulnerability and chaos, calling for robustness and stability of the network in the presence of shocks and disruptions. Resilience analysis refers to the speed at which a network returns to its equilibrium after a shock, as well as to the perturbations/shocks that can be absorbed before the network is induced into some other equilibrium (adaptivity). Connectivity is relevant here, but not often considered in spatial economics. In order to reach a unified methodological framework, attention will finally be paid to a complementary analysis of the (dynamic) concepts of vulnerability and resilience. In this light, chaos models/properties might be seen in a positive perspective, since small changes can lead to uncertain and unstable effects, but also, thanks to connectivity, to new equilibria which are not necessarily negative. Thus, the architecture of connectivity, in its interdisciplinary insights, can be considered as a fundamental (and analytical) approach for identifying vulnerability and resilience patterns in complex networks.