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What role does Socket.IO have with Node.js

I'm fairly new to the world of JS and its abundance of libraries. I'm looking to get into a project that involves network communication (sockets) between clients and a server. In a world with tons of libraries, I cannot make a decision as to which to use. I'm looking for something that will bring efficiency and stability.
I've been told that Node.js is like the middleman between you, as the developer, and Socket.IO. I've been told it's a huge framework that you may not use at least half of. I've been told that to maximize efficiency, you're better off using Socket.IO to make your own functionalities. I've done some research on my own and found that Socket.IO NEEDS Node.js and Node.js DOESN'T NEED Socket.IO. Which is completely opposite of what I was told. Then I find that most developers use both Socket.IO and Node.js at the same time?
Like I said, I'm fairly new, but I cannot find the right resources that would help me accomplish a websocket communication between a client and a server with maximum efficiency, or at least explain the difference between Socket.IO and Node.js. If anyone here could, please let me know! I would greatly appreciate it.

node.js is a general purpose javascript-based run-time environment (somewhat similar to other language runtimes like python in scope). You can create apps in it that don't even use the network. It is often used as a web server for created web apps and has a great set of tools and rich library of add-ons for doing so. It does not need socket.io.
socket.io is a specific library to enable web-socket-like communication between a client and a server (e.g. a chat room app is the canonical example). The server side of socket.io assumes a javascript run-time (because it's written in javascript) so that generally means node.js (though I'm not sure if a different JS runtime could perhaps be substituted).
You can think of node.js like the platform and socket.io like a specific tool to do a specific job that runs on that platform. You would use socket.io (on top of node.js) if you needed web socket connectivity between client and server.
You would use only node.js if you need any of the other things node is good at, but did not need websocket connectivity.
websockets themselves can be programmed on the server side without socket.io and without node.js. They could be programmed in strait C++ or in Java. But socket.io (running in node) provides a very easy way to set them up because the socket.io library covers both client and server in one library and one API and it's all in the same language (javascript). Look at the chat room app example on the socket.io site and you will be unlikely to find any other solution that can accomplish that in as few lines of code as it does and with the same interface on client and server.
If you were only setting up a websocket server (no web server or web app of any kind), you could still use node and socket.io and use it just for the websocket server and it would still be quite efficient. While node is capable of doing lots of other things, if you don't configure and install all those other things, they aren't costing you anything - they are just unused capabilities that aren't running.
I should add that one other thing the socket.io library does is it handles an auto-negotiation between client and server to find the best channel for the client and server to communicate on. If websockets are available, then socket.io will likely use them, but if web sockets are not available, socket.io has alternate methods that will work (even in older browsers). That functionality comes for free in socket.io without you even doing anything.
In case this isn't completely clear to you, websockets are typically used to provide real-time communication between client and server. While clients can ask for data from a server at any time with an ajax call or a web page request, what websockets allow is a two way real-time communication between client and server and the biggest advantage of websockets is that a server can send a client real-time data at any time while they are connected.
For example, I have a web page that receives real-time data from my server anytime the web page is open. The web page is served over the typical node.js web server installation, but the real-time data is sent from server to client over a websocket connection.
In addition, if there's a chatty conversation happening between client and server, websockets can be much more efficient than a series of ajax calls because with a websocket, a connection is opened once and used repeatedly whereas with ajax, each successive ajax call is like a new connection.

Node.js is a runtime environment. It's a javascript engine with a standard library built around asynchronous I/O. It plays the same role that Java, Python, Ruby, .NET, etc., play for many other web applications.
I've been told it's a huge framework that you may not use at least half of.
It might be true that most people never use most of the standard library, but I wouldn't think it's more true of Node.js than other runtimes. "Framework" isn't an accurate word to describe it.
I've been told that to maximize efficiency, you're better off using Socket.IO to make your own functionalities.
Whoever told you that was mistaken, or meant that to maximize efficiency, you're better off using [Node.js and] Socket.IO [instead of other solutions]. Many other non-Node.js solutions require a single thread or process per connection, which limits the number of simultaneous connections a server can handle. Node.js is built around asynchronous I/O which is better for keeping many connections open at once, and Socket.IO is a library for Node.js for using WebSockets.

TL;DR: Socket.IO can fire events in realtime between your client and server, so there is no need for you to reload the page to notice something changing. This can be used for "live" applications like collaborative drawing, live chats, online games and more!

peer to peer communication between mobile app and pc browser

I am working on a project where i need my mobile application to talk to my web browser on a pc, where both devices are connected over wifi. The app would send data which would be received by the computer browser followed by some client side code execution. The browser then may send some feedback.
My initial approach is to make the app talk to an endpoint which in turn talks to client side of the browser (javascript).
What could be the best approach to do this ?
Update
I am not sure if Socket.io is a possible solution since it requires a server to be hosted. Is it possible to solve this using sockets ?

You've now edited your question to mention P2P. That's quite hard to achieve PHONE TO BROWSER (i.e., by hard I mean 6 to 12 man-months of work - and/or plain not possible). However in MOST situations you can instantly (ie "one line of code on each platform") resolve the problem by using a service like pubnub. Much as nobody has back-ends anymore and everything is just done with parse.com or game center, networking like you mention is now just done with pubunb (or any competitor).
This is an extremely common use case problem - and everyone just uses PubNub as mentioned below or one of its competitors.
These days it couldn't be easier, just use pubnub.com
It's the world's biggest data-messaging service for a reason!
There's essentially no other realistic approach, it's so simple - a few lines of code.

So short answer would be: A real peer-to-peer (P2P) communication is currently not possible with all browsers. So instead you have the following options:
App + Server with a WebUI (maybe)
App + Chrome App (Chrome Apps can start an web server, see http://www.devworx.in/news/misc/chrome-apps-can-now-run-a-web-server-135711.html)
App + WebApp with Plugin (Flash, Silverlight or Java)
I personally would prefer solution 1.

You need a server. If you consider this problem strictly from the typical firewall point of view, a PC or a mobile device are going to ignore connections unless they initiate the connection themselves. So neither the PC nor the mobile device can start a connection with the other.
My understanding is that web browsers do not support standard sockets within javascript. You can use the analagous websocket, but sockets and websockets are not directly compatible.
You can setup a simple server on the PC, and have this server relay messages between the mobile device and the PC browser. Both the mobile device and the PC browser connect to the server. This is basically what an external service will do for you.

PeerJS is what you're looking for:
http://peerjs.com

WebRTC Data Channel server to clients UDP communication. Is it currently possible?

Is it possible to use WebRTC Data Channels on Node.js in a way that mimics the functionality of WebSockets except using UDP?
In essence I want to have a server running Node.js with which browser clients can establish a full duplex bi directional UDP connection via JavaScript.
My question is the same as this one from 8 months ago. I repost it because the only answer was :
Yes, in theory you should be able to to do this. However, you'll need a node module that supports WebRTC data channels, so that you can connect to it like any other peer. Unfortunately, scanning through the current modules, I don't see one that implements the data channel.
Any of you know of such a module ? In my search I found some node modules with the words "webrtc" and "datachannel", but they didn't look like what was needed, they looked like they were meant for specific needs.

This project is very active, and seem to undertake the mission of importing the entire WebRTC stack into node.js
There's also this project but it looks pretty inactive.
Would love to know if that was satisfying and if you're doing such a project (as in the question) please link to github :)

We have implemented the exact same thing: a server/client way of using WebRTC. Besides we also implemented data port multiplexing, so that server would only need to expose one data port for all rtcdata channels.
A quick summary of how it is achieved:
We implemented in nodejs, using wrtc library. But the same principal could be applied to other implementations.
The server exposes a control port, so that the client will exchange SDPs with the server for establishing their data channel.
To support data port multiplexing, At the server, we modify both peer's SDK, so that
Client will always connect to the same server ip:data_port
We implement a UDP data proxy inside the server, so that it can be the bridge between the server webrtc engine and the client.
The code is at: https://github.com/noia-network/webrtc-direct

Peer to Peer Connection in Windows Store App (HTML/JS)

I'd like to know if anyone has managed to set up a peer-to-peer app for the Windows Store using HTML5 and JavaScript. Basically I want app client A to be able to connect and send data to app client B via a TCP or UDP socket (the problem I'm facing seems to be irrelevant to the socket type).
My main problem is that I am unsure how to obtain a suitable IP/port which the other client would be able to connect to. It seems like there would be issues with router firewalls and whatnot, but MS claims that peer-to-peer is possible.
Any tips would be greatly appreciated, thanks.
Edit: I cannot use a third party service for communicating the data, because I want my app to be able to connect with other applications besides the one I'm writing. So something standard like TCP sockets is necessary.

Take a look at TideSDK for the desktop app development with web technology.
I don't know is TideSDK provide an API to access TCP or UDP communication, may be you could try read the docs. IMO best is you need to create a server to handle 1:1 connection between clients.
If you dont want to get mess with the server, you should get to know PubNub and Pusher

Communicate between a Rails app and a Node.js app

This question follows a previous one: Shall I use Node.js Instead of Rails for Real-time WebApps?
The question:
What's the best way of communicating between a Rails app and a Node.js app in order to take advantage of both technologies?
Thanks

Why not open a TCP socket for communication between node & RoR ?
var net = require('net');
// create TCP server
var server = net.createServer(function (socket) {
// write down socket
socket.write("Echo server\r\n");
socket.pipe(socket);
})
// start server listening on port 8124
server.listen(8124, "127.0.0.1");
And in RoR you can connect to the socket
require 'socket' # Sockets are in standard library
hostname = '127.0.0.1'
port = 8124
s = TCPSocket.open(hostname, port)
while line = s.gets # Read lines from the socket
puts line.chop # And print with platform line terminator
end
s.close # Close the socket when done
Then just write an abstraction on top of this TCP socket to synchronize your communication nicely and without requiring low level fiddling.

Why do the apps need to communicate?
If you simply need a Rails app to get some realtime data into the browser, then using a node.js server app and Socket.IO would be sufficient.
You have to remember that any Rails apps, is actually two applications, one written in Ruby running on the server, and one written in Javascript running on the client. They usually communicate over HTTP, sometimes with AJAX and sometimes not. Which part of your app needs the functionality of node.js?
If it is the case that the app deals with login, then displays a web page, and then continually refreshes that web page with real-time data, you only really get a benefit from node.js for the realtime data refreshes whether you do it with AJAX polling or with Websockets. Shared databases are a nice way for apps to communicate, but not for realtime.
To make it clear, if you are an expert in Ruby with Rails, you will be more productive if you add a node,js server app and only use it for high-volume data, such as realtime updates. You then have a hybrid web app that leverages the best of both platforms.

What about keeping Rails and use Faye?
the latest Railscast is awesome: http://railscasts.com/episodes/260-messaging-with-faye

One way is to have a common back-end database or some kind of memory storage which will act as intermediary layer between the two technologies. Popular is for example to use NoSQL DB like Redis which is fast, memory based and supports advanced data structures which are handy for this scenario. Also node.js and RoR both have a good client libraries for communication with Redis.
I would say the main problem is in initial authentication between the two separate systems which both needs to be synchronized. There are similar questions/answers related to this topic which may come useful to read, for example these two shows what are the possible ways how to solve the authentication problem.

It depends on exactly why you're separating the functionality from one to the other. Rails supports REST based separation without any extra work on your part. It's built based on resources from the ground up. That means it would be very simple for you to use an http.Client (or something like Restler) to query against it. You can certainly do the exact same the other way around, using standard Node.js routing (or something like Express) and an HTTP client for Ruby (such as Typhoeus). Though this method incurs the overhead of using a full HTTP request (not necessarily a problem if on an internal network). If you are looking for a more speedy way of communication, I'd say you could go about it using a persistant socket as Raynos suggests.
Depending on your need, I would suggest that using two separate systems creates extra code complexity, and it may be best for you to reduce it to one framework/language. I'm all for Service Oriented Design, but Rails is a pretty heavy weight and may slow down your over all response times, even with having Node.js working with it.