EdgeAdd
EdgeAdd[g, e] makes a graph by adding the edge e to the graph g.
EdgeAdd[g, {e1, e2, ...}] adds a collection of edges to g.
Examples
Add an edge to a graph:
EdgeAdd[Graph[{1 -> 2}], 2 -> 3]Add multiple edges:
EdgeAdd[CycleGraph[4], {1 -> 3, 2 -> 4}]Please visit the official Wolfram Language Reference for more details.