Depends, some graph databases have some support for graph algorithms.
I’ll also say I think graph algorithms are overrated, I mean you know the diameter of some graph: who cares? Physicists (like me back in the day) are notorious for plotting some statistics on log-log paper, seeing that the points sorta kinda fall on a line if you squint and decide that three of the points are really bug splats and then yelling “UNIVERSIALITY” and sending it to Physical Review E but the only thing that is universal is that none of them have ever heard of a statistical estimator or a significance test for power law distributions. Node 7741 is the “most central” node, but does that make a difference? Maybe if you kill the top 1% central nodes that will disrupt the terrorist network but for most of us I don’t see high quality insights coming out of graph algorithms most of the time.