Summary: An algorithm for computing the \(k\)-convex closure of a subgraph relative to a given equivalence relation \(R\) among edges of a graph is given. For general graph and arbitrary relation \(R\) the time complexity is \(O(qn^2+ mn)\), where \(n\) is the number of vertices, \(m\) is the number of edges and \(q\) is the number of equivalence classes of \(R\). A special case is an \(O(mn)\) algorithm for the usual \(k\)-convexity. We also show that Cartesian graph bundles over triangle-free bases can be recognized in \(O(mn)\) time and that all representations of such graphs as Cartesian graph bundles can be found in \(O(mn^2)\) time.