Critical journey evolving graphs

End-to-end connectivity in dynamic networks may not hold at a given point of time. Nevertheless, temporal paths (or journeys) may still exist over time and space due to the inherent evolution of networks. Large amount of work has been done to examine foremost journeys and connectivity of dynamic networks. However, as far as we know, there is still no work which can address foremost journeys calculation in continuous time under scenarios where contacts have arbitrary durations and edge traversal time is non-negligible. To this end, we propose a model named critical journey evolving graphs (CJEGs) to effectively characterize the temporal connectivity of dynamic networks. By CJEGs, a foremost journey between any pair of nodes starting at any time can be inferred directly. Accordingly, temporal connectivity metrics such as velocity, efficiency and density can be figured out. To construct CJEGs, a distributed algorithm called CJEG-PERST is developed, which can update CJEGs online adaptively with the evolution of networks, thus avoiding the hassle of heavy computation and memory overhead. We conduct extensive experiments and analysis to explore the temporal connectivity of dynamic networks by applying CJEGs to synthetic and realistic datasets, as well as making comparison with other models such as temporal reachability graphs (TRGs). Experimental results show CJEGs yield many fresh and enlightening insights into connectivity of dynamic networks. Especially, two important applications of CJEGs are further discussed, namely how to derive TRGs and calculate theoretical performance benchmark for opportunistic routing. These explorations preliminarily demonstrate the promising potentials of the CJEGs model.