The names of the functions are different.
But many of them exists in the Visio online API as well.
Not sure about ConnectedShapes though.
Here is the reference:
https://dev.office.com/reference/add-ins/visio/visio-javascript-reference-overview?product=visio
You could check out my alternative svg export. It has connectedShapes, but documentation still kind of sucks :-[
https://nbelyh.github.io/svgpublishdemo/AdvWorksOLTPSchemaVisio.html
Code for that thing (on shape click):
var shape = diagram.shapes[id];
if (shape.ConnectedTo) {
shape.ConnectedTo.forEach( function(item) {
d3.select("#" + item).selectAll("g").style("fill", "#Aff");
});
}
if (shape.ConnectedFrom) {
shape.ConnectedFrom.forEach( function(item) {
d3.select("#" + item).selectAll("g").style("fill", "#fAf");
});
}