# Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks

## TL;DR

This paper extends the formalism of stream graphs to include bipartite, weighted, and directed structures, providing a rigorous framework for modeling complex temporal networks with these features.

## Contribution

It generalizes existing graph concepts to bipartite, weighted, and directed stream graphs, ensuring consistency with classical and stream graph models.

## Key findings

- Unified formalism for bipartite, weighted, and directed stream graphs
- Generalized classical graph concepts to temporal network models
- Provides a rigorous foundation for modeling complex temporal networks

## Abstract

We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This includes in particular size, density, clique, neighborhood, degree, clustering coefficient, and transitivity. In this contribution, we show that, like graphs, stream graphs may be extended to cope with bipartite structures, with node and link weights, or with link directions. We review the main bipartite, weighted or directed graph concepts proposed in the literature, we generalize them to the cases of bipartite, weighted, or directed stream graphs, and we show that obtained concepts are consistent with graph and stream graph ones. This provides a formal ground for an accurate modeling of the many temporal networks that have one or several of these features.