Temporal Reachability Graphs

TL;DR

This paper introduces the concept of temporal reachability graphs to model and analyze time-varying networks, providing a theoretical framework, an efficient computation algorithm, and demonstrating their practical utility on real datasets.

Contribution

The paper presents a novel formalization of temporal reachability graphs, an efficient algorithm for their computation, and showcases their application to real-world network data.

Findings

Defines the concept of (tau, delta)-reachability graphs for time-varying networks.

Provides an algorithm for efficient computation of these graphs.

Demonstrates the utility of reachability graphs in analyzing real and synthetic datasets.

Abstract

While a natural fit for modeling and understanding mobile networks, time-varying graphs remain poorly understood. Indeed, many of the usual concepts of static graphs have no obvious counterpart in time-varying ones. In this paper, we introduce the notion of temporal reachability graphs. A (tau,delta)-reachability graph} is a time-varying directed graph derived from an existing connectivity graph. An edge exists from one node to another in the reachability graph at time t if there exists a journey (i.e., a spatiotemporal path) in the connectivity graph from the first node to the second, leaving after t, with a positive edge traversal time tau, and arriving within a maximum delay delta. We make three contributions. First, we develop the theoretical framework around temporal reachability graphs. Second, we harness our theoretical findings to propose an algorithm for their efficient computation. Finally, we demonstrate the analytic power of the temporal reachability graph concept by applying it to synthetic and real-life datasets. On top of defining clear upper bounds on communication capabilities, reachability graphs highlight asymmetric communication opportunities and offloading potential.