Weighted, Bipartite, or Directed Stream Graphs for the Modeling of 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.

Computing Betweenness Centrality in Link Streams

“…We considered here streams with link (and node) presence times equal to unions of disjoint closed intervals (including singletons); another extension would be to consider more general cases, like for instance unions of disjoint closed or open intervals. Also, weighted and/or directed stream graphs and link streams [17] lead to more complex concepts of shortest fastest paths, and our definitions of volumes may be extended to these cases. Conversely, one may consider more specific situations, like discrete time streams, or link stream with instantaneous links only.…”

Do you trade with your friends or become friends with your trading partners? A case study in the G1 cryptocurrency

“…As we will see in section 3, although the data is rather simple at first glance, the proper modeling of interactions is challenging and no unique, commonly accepted approach exists. We leverage here the recently introduced link stream model, which captures both the temporal and structural nature of data [25] [26]. We start our analysis with basic metrics targetting the questions above and we define link stream concepts as we need them in the analysis.…”

“…Classical methods such as static graphs or time series simplify data and information is lost in the process. In this paper, we use link streams, rencently introduced in [25] and [26]. Below, we give basic link stream notations and we refer the interested reader to these papers for more details.…”

“…A key concept in graph theory is the one of neighborhoods. For a directed link stream L = (T, V, E) the definition of the neighborhood of node v ∈ V , as given in [26], is the following cluster:…”

Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring

“…If C is a class of static graphs, then the two most obvious ways of defining a temporal analog to C are (i) including all temporal graphs whose underlying graph is in C or (ii) including all temporal graphs that have all of their layers in C (see, for instance, [18]). Most applied research that has employed a notion of bipartiteness in temporal graphs [1,28,39] has defined it using the underlying graph, seeking to model relationships between two different types of entities. This is certainly appropriate as long as the type of an entity is not itself time-varying.…”