You can just loop over your places/transitions and links and create JointJS elements/links. Something like:
_.each(json1.places, function(p) {
graph.addCell(new joint.shapes.pn.Place({
id: 'place' + p.id,
position: { x: p.x, y: p.y },
size: { width: p.width, height: p.height }
}));
});
_.each(json1.transitions, function(t) {
graph.addCell(new joint.shapes.pn.Transition({
id: 'transition' + t.id,
position: { x: t.x, y: t.y },
size: { width: t.width, height: t.height },
attrs: { '.label': { text: t.label } }
}));
});
_.each(json1.ptlinks, function(l) {
graph.addCell(new joint.dia.Link({
source: { id: 'place' + l.src },
target: { id: 'transition' + l.dst },
labels: [ { position: .5, attrs: { text: { text: l.expr } } } ]
}));
});
_.each(json1.tplinks, function(l) {
graph.addCell(new joint.dia.Link({
source: { id: 'transition' + l.src },
target: { id: 'place' + l.dst },
labels: [ { position: .5 } ]
}));
});