Attach buttons to graph elements

I've created an app using the app designer that creates a graph from user inputs with buttons for adding nodes and edges separately, updating the graph each time a node or edge is added. I want each node and edge to be clickable buttons which open a new dialogue in which additional data can be inputted and viewed in the form of a table or database. Any ideas on how I could achieve this?

The inputs occur like this currently in case it's helpful:

function NewNodeButtonPushed(app, event)
%get basic node data from user
nodetemp = inputdlg(["Node Name", "Latitude", "Longitude"], "Node Details");
%add code to start 
nodeinp = addvars(cell2table(transpose(nodetemp),'VariableNames',{'Name','Latitude', ...
    'Longitude'}), app.index, 'before', 1,'NewVariableNames',{'Code'});
%update graph with node data
app.NodeTable=[app.NodeTable; nodeinp];
%app.G=graph(app.EdgeTable,app.NodeTable);
app.G=addnode(app.G,nodeinp);
%display graph
plot(app.UIAxes,app.G,'NodeLabel',app.G.Nodes.Name,'EdgeLabel',app.G.Edges.Distance)%plot graph
app.UITable.Data = app.NodeTable;
app.index = app.index + 1; %increment node counter
end

[Voss]

Calling plot on a graph returns a GraphPlot object with properties described here: https://www.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.graphplot-properties.html

I would first try setting a ButtonDownFcn on the GraphPlot object, and verify that clicks on and near the graph are recognized appropriately.

Another option is to use a UIContextMenu on the GraphPlot object, with menu items for various operations.

[Timothy]

Is it possible to create callbacks for the nodes and edge presses or is it better to switch off the hit test property and treat it like a regular axes?