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The statistical analysis of structured spatial point process data where the event locations are determined by an underlying spatially embedded relational system has become a vivid field of research. Despite a growing literature on different extensions of point process characteristics to linear network domains, most software implementations remain restricted to either directed or undirected network structures and are of limited use for the analysis of rather complex real-world systems consisting of both undirected and directed parts. Formalizing the network through a graph theoretic perspective, this paper discusses a complementary approach for the analysis of network-based event data through generic network intensity functions and gives a general introduction to the intensitynet package implemented in R covering both computational details and applications. By treating the edges as fundamental entities, the implemented approach allows the computation of intensities and other related values related to different graph structures containing undirected, directed, or a combination of both edges as special cases. The package includes characteristics for network modeling, data manipulation, intensity estimation, computation of local and global autocorrelation statistics, visualization, and extensions to marked point process scenarios. All functionalities are accompanied by reproducible code examples using the chicago data as toy example to illustrate the application of the package.