Topological analysis of large networks

摘要

This paper offers new concepts for ordering of large surface networks, which so far have essentially been treated using a combinatorial approach rather than relying on their structural interdependence expressed by laws of geometry. It is shown that the Jordan curve theorem can serve as a powerful algorithm to define, for example, the relationship of a network point to the rest of the whole network. Combining this topological principle with utilization of rich metrical network properties, the analysis transforms a network to a strictly ordered set with a distinct hierarchy of components. Every point is supplied with proposed topological indices reflecting the belonging of a point to its defined environment, or topological group(s). Becoming objects of computation and consideration, the groups themselves are attributed to the corresponding coherent and/or girded groups of the following degree of complexity. The numerous point set is now replaced by the essentially lesser natural aggregation of defined images and the created database files gain a great accessibility.