Complexity and Spatial Networks

In the past decade, complexity has become an important and fascinating domain for advanced research on non-linear dynamics, in which a multiplicity of scientific fields are involved (physics, life sciences, social sciences, economics, geography, and so forth). Complex systems analysis refers to research at the dynamic interface of – or the interaction between – small or micro-elements of a system that are interconnected and determine a macro-level of operation of the system that is not just the sum of the micro-elements. As a result of self-organizing forces among interacting micro-units, a dynamic network configuration may emerge that displays its own dynamics, ranging from ‘butterfly’ effects to scale-free evolution, or from bifurcations with unexpected phase transitions to preferential attachment in small-world networks. The complexity movement has also had far-reaching impacts on dynamics research in the spatial sciences. The space-economy is often interpreted as a standard well-functioning economic system enriched with the element of space. But space is not just an additional dimension of the economy: it forms an intrinsic feature of any geographic-economic system and may lead to the emergence of complex non-linear and interactive behaviours and processes in a geographic setting. The foundation for an interpretation of the space-economy as an interdependent complex set of economic relationships – at different geographic scales and with a variety of time dimensions involved – can be found in the ‘first law of geography’ formulated by Tobler (1970) who stipulates that everything in space is related to everything else, but near things are more related than distant things. The solidity of this law needs to be reconsidered in the light of recent advances in complexity and network theory. In particular, the latest findings in network theory show how – for certain network typologies – distant things can be related by means of ‘hubs’ or ‘egos’ (preferential nodes/attractors). Spatial networks appear to exert a dynamic impact on an organized space. One of the striking features in the modern space-economy has been the simultaneous occurrence of spatial dynamics (both fast and slow dynamics) and spatial inertia (e.g. persistent welfare disparities between regions). Regions and cities are apparently operating in a complex force field, with asynchronously emerging key factors that impact on regional or urban development in different ways and with different growth paces. This rapidly changing scene of regional and urban development has called for new research departures, such as: a reliance on experimental psychology/sociology, design of learning principles for decision makers (based on evolutionary biology), integration of ethical and sociological notions in policies for a multi-cultural society, etc. Consequently, regional and urban research has become richer in scope, with more emphasis on interdisciplinarity, complexity, synergy among research methodologies, conflict management principles, adaptive and evolutionary (notably, learning) behaviour, and increasing interest in the great potential offered by the cognitive sciences. This book aims to offer a panoramic view of recent advances in spatial complexity, in order to enhance our understanding of complex spatial networks by simplicity in terms of the basic driving forces of systemic impacts, as well as in terms of modelling such systems. Simple models mapping out the evolution of complex networks are undoubtedly a key issue in spatial economic research.