MEASURING THE QUALITY OF THE NAVIGATION IN WEB SITES USING THE CLONING RELATION ANASTASIU POPESCU, Doru University of Pite¸sti, Romania Faculty of Mathematics and Computer Science dopopan@gmail.com Abstract In this paper, a new method of calculating the WSC number is being presented, used for measuring the quality of navigation in a web site. The method of calculating this number is based on using a relation between the web pages of the web site and constructing a reduced navigation graph. Keywords: Navigation, Relation, Tag, HTML, Web Site AMS Classification: Primary 68U35, 68W01; Secondary 68Q60, 68N30, 68M11, 68N03 1. Introduction The results of this paper refer to web sites which contain web pages consisting of HTML tags, saved in files with the extensions .html and .htm. Next, we name these web pages. On one hand, the number of web application built using this kind of web pages is very large; on the other hand, the web applications can contain a very large number of web pages. Navigating in these web sites is an especially important mechanism. There exist different methods of measuring the navigation in these sites. In the papers [10] and [11] such methods are being described, from which we will next use the WSC number (Web Site Complexity). Calculating the WSC number involves using the entire navigation graph (which most of the times has a very large number of nodes). In the following sections, we will introduce a method of calculating it, which uses an equivalence relation between the web pages of the web site, introduced in [2], [4], [6] and a reduced navigation graph, presented in [7]. 2. Defining a relation between two web pages Next, we will consider a web application with the set of web pages P={p 1 , p 2 , ..., p n } and a set TG of tags. For any web page p i from P, 1≤i≤n, we write T i the sequence of tags from p i , which are not in TG (the order in which these are encountered is important). Definition. Let TG be a set of tags, p i and p j two web pages P, 1≤i,j≤n. We say that p i and p j are cloned and we write p i Cp j , if T i and T j coincide. 5