Spatial Resilience in Networks

Abstract

In recent times, and particularly since the advent of the internet, graph theory (and its sub-discipline of network analysis) has taken on a new importance as one of the branches of mathematics that is best suited to exploring questions of connectivity and relationality. Just about anything that involves exchanges between manageable numbers of distinct entities, in real or conceptual space, can be analysed as a net- work problem. This is not to say that network approaches should be applied in all cases; there is a set of problems for which network approaches are ideal, and a set of problems for which they are not. As a conceptual and analytical tool for the study of social-ecological systems, however, network analysis can not be ignored. Networks consist of two primary elements, termed nodes (synonymous with ver- tices, locations, and actors) and links (edges, bonds, ties). The nodes of the network are typically comprised of discrete elements like towns, individuals, protected areas, or computer terminals. The links or edges capture the connections of nodes to one another. Links describe such things as roads, telephone lines, personal interactions, the movements of organisms, or virtually any other kind of exchange or flow that occurs directly between nodes. Links may be unidirectional, as in a river, or bidi- rectional, as in a road; they may have a spatially explicit or a spatially independent nature; they may exist permanently or only for short periods; and they may carry high or low volumes.