Title: Second-order and local characteristics of network intensity functions,
Abstract: The last decade has witnessed an increase of interest in the spatial analysis
of structured point patterns over networks whose analysis is challenging
because of geometrical complexities and unique methodological problems. In this
context, it is essential to incorporate the network specificity into the
analysis as the locations of events are restricted to areas covered by line
segments. Relying on concepts originating from graph theory, we extend the
notions of first-order network intensity functions to second-order and local
network intensity functions. We consider two types of local indicators of
network association functions which can be understood as adaptations of the
primary ideas of local analysis on the plane. We develop the node-wise and
cross-hierarchical type of local functions. A real dataset on urban
disturbances is also presented.