Yes graph algorithms are actively researched. You can browse arxiv.org and see plenty of recent submissions: https://arxiv.org/search/?query=Graph&source=header

Yes graph algorithms are actively researched. You can browse arxiv.org and see plenty of recent submissions: https://arxiv.org/search/?query=Graph&source=header&searchtype=all https://arxiv.org/search/?query=Graph&source=header&searchty... For applications, compilers need graph coloring. Task schedulers need graph cuts. Since these are NP complete there is plenty of room for research on specific implementations with various heuristics.