Random chat with 2 users at a time (Socket.io)

I just started learning NodeJS and Socket.io ... Until now I have this demo code, from official socket.io site:

http://ift.tt/1vdijml

I am able to get the unique client's ID of each user (socket) which connects, I am still trying to figure out, How can I make my code to only connect with 1 random user at a time when somebody runs the application. I just want to make random chat like Omegle http://www.omegle.com/

Only 2 users should randomly connect and chat with each other till they re-run the app, if they come back they should get connected with someone else who is in the online queue.

What changes do I need to do to have a similar behaviour?

Here is my code so far:

Index.js

// Setup basic express server
var express = require('express');
var app = express();
var server = require('http').createServer(app);
var io = require('socket.io')(server);
var port = process.env.PORT || 3000;

server.listen(port, function () {
  console.log('Server listening at port %d', port);
});

// Routing
app.use(express.static(__dirname + '/public'));

// Chatroom

var numUsers = 0;

io.on('connection', function (socket) {
    console.log('User '+socket.id + ' connected');
  var addedUser = false;

  // when the client emits 'new message', this listens and executes
  socket.on('new message', function (data) {
    // we tell the client to execute 'new message'
    socket.broadcast.emit('new message', {
      username: socket.username,
      message: data
    });
  });

  // when the client emits 'add user', this listens and executes
  socket.on('add user', function (username) {
    if (addedUser) return;

    // we store the username in the socket session for this client
    socket.username = username;
    ++numUsers;
    addedUser = true;
    socket.emit('login', {
      numUsers: numUsers
    });
    // echo globally (all clients) that a person has connected
    socket.broadcast.emit('user joined', {
      username: socket.username,
      numUsers: numUsers
    });
  });

  // when the client emits 'typing', we broadcast it to others
  socket.on('typing', function () {
    socket.broadcast.emit('typing', {
      username: socket.username
    });
  });

  // when the client emits 'stop typing', we broadcast it to others
  socket.on('stop typing', function () {
    socket.broadcast.emit('stop typing', {
      username: socket.username
    });
  });

  // when the user disconnects.. perform this
  socket.on('disconnect', function () {
    if (addedUser) {
      --numUsers;


      // echo globally that this client has left
      socket.broadcast.emit('user left', {
        username: socket.username,
        numUsers: numUsers
      });
    }
    //Status server the client gone
    console.log('User '+socket.id + ' disconnected');

  });
});

Code examples or guidance from an expert will be really helpful for noob like me.

UPDATE: Added Client site code, main.js

$(function() {
  var FADE_TIME = 150; // ms
  var TYPING_TIMER_LENGTH = 400; // ms
  var COLORS = [
    '#e21400', '#91580f', '#f8a700', '#f78b00',
    '#58dc00', '#287b00', '#a8f07a', '#4ae8c4',
    '#3b88eb', '#3824aa', '#a700ff', '#d300e7'
  ];

  // Initialize variables
  var $window = $(window);
  var $usernameInput = $('.usernameInput'); // Input for username
  var $messages = $('.messages'); // Messages area
  var $inputMessage = $('.inputMessage'); // Input message input box

  var $loginPage = $('.login.page'); // The login page
  var $chatPage = $('.chat.page'); // The chatroom page

  // Prompt for setting a username
  var username;
  var connected = false;
  var typing = false;
  var lastTypingTime;
  var $currentInput = $usernameInput.focus();


  //Own Global

  var room = '';

  var socket = io();

  function addParticipantsMessage (data) {
    var message = '';
    if (data.numUsers === 1) {
     // message += "there's 1 participant";
     // Status Message
        message += "Waiting to connect with someone";

    } else {
     // message += "there are " + data.numUsers + " participants";
     //Status message update
      message = "You are connected to a stranger! Say Hey!";
    }
    log(message);
  }

  // Sets the client's username
  function setUsername () {
    username = cleanInput($usernameInput.val().trim());

    // If the username is valid
    if (username) {
      $loginPage.fadeOut();
      $chatPage.show();
      $loginPage.off('click');
      $currentInput = $inputMessage.focus();

      // Tell the server your username
      socket.emit('add user', username);

      // Own
      socket.emit('login', {'username' : 'Faizan'});

    }
  }

  // Sends a chat message
  function sendMessage () {
    var message = $inputMessage.val();
    // Prevent markup from being injected into the message
    message = cleanInput(message);
    // if there is a non-empty message and a socket connection
    if (message && connected) {
      $inputMessage.val('');
      addChatMessage({
        username: username,
        message: message
      });
      // tell server to execute 'new message' and send along one parameter
      socket.emit('new message', message);
    }
  }

  // Log a message
  function log (message, options) {
    var $el = $('<li>').addClass('log').text(message);
    addMessageElement($el, options);
  }

  // Adds the visual chat message to the message list
  function addChatMessage (data, options) {
    // Don't fade the message in if there is an 'X was typing'
    var $typingMessages = getTypingMessages(data);
    options = options || {};
    if ($typingMessages.length !== 0) {
      options.fade = false;
      $typingMessages.remove();
    }

    var $usernameDiv = $('<span class="username"/>')
      .text(data.username)
      .css('color', getUsernameColor(data.username));
    var $messageBodyDiv = $('<span class="messageBody">')
      .text(data.message);

    var typingClass = data.typing ? 'typing' : '';
    var $messageDiv = $('<li class="message"/>')
      .data('username', data.username)
      .addClass(typingClass)
      .append($usernameDiv, $messageBodyDiv);

    addMessageElement($messageDiv, options);
  }

  // Adds the visual chat typing message
  function addChatTyping (data) {
    data.typing = true;
    data.message = 'is typing';
    addChatMessage(data);
  }

  // Removes the visual chat typing message
  function removeChatTyping (data) {
    getTypingMessages(data).fadeOut(function () {
      $(this).remove();
    });
  }

  // Adds a message element to the messages and scrolls to the bottom
  // el - The element to add as a message
  // options.fade - If the element should fade-in (default = true)
  // options.prepend - If the element should prepend
  //   all other messages (default = false)
  function addMessageElement (el, options) {
    var $el = $(el);

    // Setup default options
    if (!options) {
      options = {};
    }
    if (typeof options.fade === 'undefined') {
      options.fade = true;
    }
    if (typeof options.prepend === 'undefined') {
      options.prepend = false;
    }

    // Apply options
    if (options.fade) {
      $el.hide().fadeIn(FADE_TIME);
    }
    if (options.prepend) {
      $messages.prepend($el);
    } else {
      $messages.append($el);
    }
    $messages[0].scrollTop = $messages[0].scrollHeight;
  }

  // Prevents input from having injected markup
  function cleanInput (input) {
    return $('<div/>').text(input).text();
  }

  // Updates the typing event
  function updateTyping () {
    if (connected) {
      if (!typing) {
        typing = true;
        socket.emit('typing');
      }
      lastTypingTime = (new Date()).getTime();

      setTimeout(function () {
        var typingTimer = (new Date()).getTime();
        var timeDiff = typingTimer - lastTypingTime;
        if (timeDiff >= TYPING_TIMER_LENGTH && typing) {
          socket.emit('stop typing');
          typing = false;
        }
      }, TYPING_TIMER_LENGTH);
    }
  }

  // Gets the 'X is typing' messages of a user
  function getTypingMessages (data) {
    return $('.typing.message').filter(function (i) {
      return $(this).data('username') === data.username;
    });
  }

  // Gets the color of a username through our hash function
  function getUsernameColor (username) {
    // Compute hash code
    var hash = 7;
    for (var i = 0; i < username.length; i++) {
       hash = username.charCodeAt(i) + (hash << 5) - hash;
    }
    // Calculate color
    var index = Math.abs(hash % COLORS.length);
    return COLORS[index];
  }

  // Keyboard events

  $window.keydown(function (event) {
    // Auto-focus the current input when a key is typed
    if (!(event.ctrlKey || event.metaKey || event.altKey)) {
      $currentInput.focus();
    }
    // When the client hits ENTER on their keyboard
    if (event.which === 13) {
      if (username) {
        sendMessage();
        socket.emit('stop typing');
        typing = false;
      } else {
        setUsername();
      }
    }
  });

  $inputMessage.on('input', function() {
    updateTyping();
  });

  // Click events

  // Focus input when clicking anywhere on login page
  $loginPage.click(function () {
    $currentInput.focus();
  });

  // Focus input when clicking on the message input's border
  $inputMessage.click(function () {
    $inputMessage.focus();
  });

  // Socket events

  //Own Events
  var room;
      socket.on('connect', function (data) { // we are connected, should send our name
        connected = true;

        room = data.room;
        username = "faizan";
        console.log("i am in client connected");
        if (username) socket.emit('login', {'username' : 'Faizan'});
    });

        socket.on('chat start', function(data) {
    //  show_chat_window(data.name); // some method which will show chat window
        console.log("u r chatting with" + data.name);
        });

            socket.on('chat end', function(data) {
            console.log("ur chat ended with " + data.name);

            //hide_chat_window(); // this will close chat window and alert user that the peer ended chat
            socket.leave(room); // it's possible to leave from both server and client, hoever it is //better to be done by the client in this case
            room = '';
        });

            socket.on('disconnect', function(data) { // handle server/connection falling
            console.log('Connection fell or your browser is closing.');
        });

            var send_message = function(text) { // method, which you will call when user hits enter in //input field
            addChatMessage(data);
            if (connected) socket.emit('message', {'text': text});
        };

            var leave_chat = function() { // call this when user want to end current chat
            if (connected) {
                socket.emit('leave room');
                socket.leave(room);
                room = '';
                console.log("user wants to end the chat");
            }
        };

// Original Code            

  // Whenever the server emits 'login', log the login message
  socket.on('login', function (data) {
    connected = true;
    // Display the welcome message
    var message = "Welcome to Socket.IO Chat – ";
    log(message, {
      prepend: true
    });
    addParticipantsMessage(data);
  });

  // Whenever the server emits 'new message', update the chat body
  socket.on('new message', function (data) {
    addChatMessage(data);
  });

  // Whenever the server emits 'user joined', log it in the chat body
  socket.on('user joined', function (data) {
    log(data.username + ' joined');
    addParticipantsMessage(data);
  });

  // Whenever the server emits 'user left', log it in the chat body
  socket.on('user left', function (data) {
    log(data.username + ' left');
    addParticipantsMessage(data);
    removeChatTyping(data);
  });

  // Whenever the server emits 'typing', show the typing message
  socket.on('typing', function (data) {
    addChatTyping(data);
  });

  // Whenever the server emits 'stop typing', kill the typing message
  socket.on('stop typing', function (data) {
    removeChatTyping(data);
  });
});

Thanks in advance