ele.component()

[maxkfranz]

eles.components() gives all components of the elements in the calling collection. It would be nice to have ele.component() that gives the component of a node or an edge.

ele.component() would have to take into account all the elements in the graph --- i.e. you can't specify a subset of elements to consider. For those cases, it's better to use eles.components().

[shabble]

is this as simple as something like:

function (ele) {
    let compEles = new Set(); 
    cy.elements().breadthFirstSearch({ root: ele, visit: (v) => { compEles.add(v) }} );
   return compEles;
}

or is there some better algorithm to use?

If it's as simple as above I can try to look at making a PR for it.

[maxkfranz]

More or less. You'd use a new cy.collection() and merge() for internal functions for performance. It's basically the existing ele.components() function implementation but only using one node as input rather than all nodes.