Temporal Connectivity and Path Computation for Stream Graph

By

Léo Rannou

EDITE de Paris, LIP6, Thalès SIX - ThereSIS

Abstract

Keywords:stream graphs, temporal networks, time-varying graphs, dynamic graphs,dynamic networks, interactions, graphs, networks, connected components, temporalpaths, algorithms, link streams
For a long time, structured data and temporal data have been analysed separately. Many real world complex networks have a temporal dimension, such as contacts between individuals or financial transactions. Graph theory provides a wide set of tools to model and analyze static connections between entities. Unfortunately, this approach does not take into account the temporal nature of interactions.  Stream graph theory is a formalism to model highly dynamic networks in which nodes and/or links arrive and/or leave over time.  The number of applications of stream graph theory has risen rapidly, along with the number of theoretical concepts and algorithms to compute them. Several theoretical concepts such as connected components and temporal paths in stream graphs were defined recently, but no algorithm was provided to compute them.  Moreover, the algorithmic complexities of these problems are unknown, as well as the insight they may shed on real-world stream graphs of interest. In this thesis, we present several solutions to compute notions of connectivity and path concepts in stream graphs. We also present alternative representations - data structures designed to facilitate specific computations - of stream graphs. We provide implementations and experimentally compare our methods in a wide range of practical cases. We show that these concepts indeed give much insight on features of large-scale datasets. Straph, a python library, was developed in order to have a reliable library for manipulating, analysing and visualising stream graphs, to design algorithms and models, and to rapidly evaluate them.

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