Cacher is the code snippet organizer for pro developers

/**
 * var 'polygon' created elsewhere
*/

//create bounds
var bounds = new google.maps.LatLngBounds();
var paths = polygon.getPaths();
var path;

for (var p = 0; p < paths.getLength(); p++) {
    path = paths.getAt(p);
    for (var i = 0; i < path.getLength(); i++) {
        bounds.extend(path.getAt(i));
    }
}

//get center
bounds.getCenter();