JavaScript LinkedList Example

LinkedList.js

//I wanted a more elegant linkedlist example than the others, so purely for academic purposes I created one.

var LinkedList = function(e){

   var that = {}, first, last;

   that.push = function(value){
      var node = new Node(value);
      if(first == null){
         first = last = node;
      }else{
         last.next = node;
         last = node;
      }
   };

   that.pop = function(){
      var value = first;
      first = first.next;
      return value;
   };

   that.remove = function(index) {
      var i = 0;
      var current = first, previous;
      if(index === 0){
          //handle special case - first node
          first = current.next;
      }else{
          while(i++ < index){
              //set previous to first node
              previous = current;
              //set current to the next one
              current = current.next
          }
          //skip to the next node
          previous.next = current.next;
      }
      return current.value;
   };

   var Node = function(value){
      this.value = value;
      var next = {};
   };

   return that;
};


var linkedList = new LinkedList();
linkedList.push(1);
linkedList.push(2);
linkedList.push(3);
linkedList.push(4);

linkedList.remove(0);

console.log(linkedList.pop());
console.log(linkedList.pop());
console.log(linkedList.pop());

Your that = {} and usage of new is confusing intention. Should probably be either that = this or just list = LinkedList();

var next = {}; is unused.

var list = function (e) {
var self = this;
var first, last, head;

    self.insert = function (value) {
        var node = new Node(value);
        if (first == null) {
            first = last = node;
        } else {
            var head = first;
            while (head.next != null) {
                head = head.next;
            }
            head.next = node;
            last = head.next;
        }
    }

    self.show = function () {
        var head = first;
        while (head != null) {
            console.log(head.value);
            head = head.next;
        }
    }

    self.remove = function (value) {
        var found = false;
        var head = first;
        while (head != null) {
            if (first.value == value) {
                prev = head = first = first.next;
                found = true;
            } else {
                if (head.value == value) {
                    found = true;
                    prev.next = head.next;
                }
                prev = head;
                head = head.next;                            
            }
        }

        if (!found) {
            console.log("#" + value + " not found");
        }
    }

    self.update = function (value, newValue) {
        var head = first;
        while (head != null) {
            if (head.value == value) {
                head.value = newValue;
            }
            head = head.next;
        }

    }

    var Node = function (value) {
        this.value = value;
        var next = {};
    }

    return self;
};

var list = new list();
list.insert(1);
list.insert(2);
list.insert(3);
list.insert(4);

list.show();
console.log("____________________________");

list.update(2, 5);           
list.show();
console.log("____________________________");

list.remove(3);
list.show();