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1.9.8
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VeloGraphX
High-performance dynamic graph analytics in C++20
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Dynamic connected components keeps track of graph connectivity while edges are added or removed. Instead of recomputing all components after every update, a maintained algorithm can reuse existing connectivity state and update only what is necessary.
VeloGraphX provides exact maintained connectivity for evolving graphs through its dynamic connected-components implementation.
For an undirected graph, connected components partition vertices into groups where every pair of vertices in the same component is connected by a path. When the graph changes, insertions can merge components and removals can potentially split them.
A dynamic connected-components algorithm must update that partition correctly after each graph change. VeloGraphX treats the maintained result as an exact connectivity contract rather than an approximation.
An inserted edge can often be handled locally because it either connects vertices that are already in the same component or joins two components. A removed edge is more challenging because the engine must determine whether an alternative path still connects the affected vertices or whether a component has actually split.
This is a common theme in dynamic graph algorithms: the number of updated edges alone does not fully describe the amount of affected analytical work.
The maintained connected-components implementation is part of the public incremental API under include/velographx/incremental/connected_components.hpp.
It runs over the same evolving-graph substrate used by the rest of VeloGraphX, so connectivity maintenance can be combined with repeated update batches, canonical graph consolidation, and other maintained analytics.
VeloGraphX documents connected components as exact maintained connectivity. The project distinguishes exact-result algorithms from PageRank-related maintenance, which uses a residual/tolerance contract instead.
That explicit contract is useful for applications where changing graph structure must not silently change result semantics.
1.9.8