Second-order and local characteristics of network intensity functions

Abstract

The last decade has witnessed an increase of interest in the spatial analysis of structuredpoint patterns over networks whose analysis is challenging because of geometricalcomplexities and unique methodological problems. In this context, it is essential toincorporate the network specificity into the analysis as the locations of events arerestricted to areas covered by line segments. Relying on concepts originating fromgraphtheory,weextendthenotionsoffirst-ordernetworkintensityfunctionstosecond-order and local network intensity functions. We consider two types of local indicatorsofnetworkassociationfunctionswhichcanbeunderstoodasadaptationsoftheprimaryideas of local analysis on the plane. We develop the nodewise and cross-hierarchicaltype of local functions. A real data set on urban disturbances is also presented.