MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM

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MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM ( mathematics-behind-google-pagerank-algorithm )

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2.1 Graph Theory CHAPTER II BACKGROUND MATHEMATICS One of the essential foundations necessary for representing the Internet net- work is graph theory. Graph theory is the study of graphs, mathematical struc- tures that model pairwise relations between objects. The first paper that shows graph theory was the ”Seven Bridges of Königsberg” by Euler (1759). The Königsberg problem involved trying to find a path that traveled each of the seven bridges connecting four landmasses, crossing each bridge only once. There Euler (1759) laid the groundwork for the field by reducing the bridge problem to a graph, where the landmasses were vertices and the bridges were edges. Graphs may be made up of vertices and edges, where vertices are points on the graph and the edges are the lines that connect them. An undirected graph makes no distinctions of the direction of an edge between two vertices; while in a directed graph, edges have directions. A graph is made up of two sets, a set of vertices, V, and a set of pairs of vertices, the edges, E. The undirected graph in Figure 2.1 can be written as: V (G) = {A, B, C, D, E, F } E(G) = {(A,B),(A,C),(A,D),(B,D),(C,D),(C,E),(D,E),(D,F),(E,F)} (II.1) 2

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