Second-order and local characteristics of network intensity functions

TL;DR

This paper extends the analysis of spatial point patterns on networks by developing second-order and local network intensity functions, incorporating network-specific features for more detailed spatial analysis.

Contribution

It introduces second-order and local network intensity functions based on graph theory, enhancing the analysis of point patterns on complex networks.

Findings

Development of node-wise local functions

Introduction of cross-hierarchical local functions

Application to urban disturbance data

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.