We discuss a variety of extensions of connected components in temporal graphs, focusing on extensions using connectivity over time through temporal paths (or journeys). Starting with components induced by temporal sources or sinks, we build up to components induced by multiple sources or sinks, and eventually components where all vertices are sources and sinks, i.e. temporally connected components. The cases of bounded components (i.e. defined on time windows), and open or closed components, are also considered. Our contributions mainly include structural results on the number of components, and algorithmic and complexity results of corresponding decision problems. Several new NP-completeness proofs are provided while exploring the boundaries between easy and difficult problems.
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Balev et al. (2024) studied this question.
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