  We introduce the notion of intensity reweighted moment pseudostationary point
processes on linear networks. Based on arbitrary general regular linear network
distances, we propose geometrically corrected versions of different
higher-order summary statistics, including the inhomogeneous empty space
function, the inhomogeneous nearest neighbour distance distribution function
and the inhomogeneous $J$-function. We also discuss their non-parametric
estimators. Through a simulation study, considering models with different types
of spatial interaction, we study the performance of our proposed summary
statistics. Finally, we make use of our methodology to analyse two datasets:
motor vehicle traffic accidents and spider data.
