You can use `/users/{ids}/associated`

Try it for [your network account](http://api.stackexchange.com/docs/associated-users#ids=4337810&filter=default&run=true)

> Returns all of a user's associated accounts, given their account_ids  in {ids}.  
>{ids} can contain up to 100 semicolon delimited ids, to find ids programmatically look for account_id on user objects.  
>You can filter the network_users returned by this method with the types parameter. Specify, semicolon delimited, main_site or meta_site to filter by site.  
> This method returns a list of network_users.


I created a [jsFiddle](http://jsfiddle.net/ugz6fhks/) to demonstrate the possible usage and included that as well in the stack snippet found below.

For completeness this is the code:

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->


    function load(id) {
        var server = 'http://api.stackexchange.com/2.2',
            path = '/users/' + id + '/associated' ,
            filter = 'filter=!*LCuYQnqAGqQ14Mr';
        $.get(server + path + '?' + filter,  function(data) {
            for(var i=0; i<data.items.length; i++) {
                var u=data.items[i];
                $('#r').append(
                    $('<a></a>')
                    .text(u.site_name)
                    .prop('href', u.site_url+'/users/'+ u.user_id ));
            }
        });
    }

    $('#load').on('click', function(e) {
        load($('#networkid').val());
        return false;
    });



<!-- language: lang-css -->

    a {
          display: block;
    }


<!-- language: lang-html -->

    <script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
    <div>
        <label for="networkid">Your SE network ID</label>
        <input id="networkid" type="text" value="4337810" />
        <input id="load" type="button" value="Load" />
    </div>
    <div id='r'>
    </div>

<!-- end snippet -->