Methods and apparatus for ranking a node in a network having a plurality of interconnecting nodes

• US 20080075014A1
• Filed: 09/22/2006
• Published: 03/27/2008
• Est. Priority Date: 09/22/2006
• Status: Active Grant

• Current Assignee: Hong Kong Polytechnic University
• Original Assignee: Hong Kong Polytechnic University
• Inventors: Jiang, Bin
• Granted Patent: US 7,688,748 B2
• Time in Patent Office: Days
• US Class Current: 370/252
• CPC Class Codes: G06F 16/951 Indexing; Web crawling techniques

Abstract

PageRank (PR) is used by web search engine Google in ranking individual web pages. However, it is known that this value is also easily manipulated by methods known as spoofing. Further, the calculation of PR will require iterative cycles of computations to achieve a “steady” value. This would mean that huge computation resources are required to obtain reasonably reliable PR values for various web pages. This invention provides relatively accurate and simple methods for ranking the importance of a node in a network. The web graph or the network is first represented by an incidence matrix or a representation matrix W. The matrix W is then self-multiplied to obtain flow matrix. The flow capacity, or the rank of each node, is then obtained from the flow matrix.

Claims

1. A method of ranking a node within a network of a plurality of interconnected nodes, each node having a connection with at least one other node in the network, the method including the steps of:

constructing a representation matrix, wherein each element of the representation matrix represents the connection between each of the interconnected nodes;

obtaining a flow matrix by multiplying the representation matrix by itself, wherein each element of the flow matrix represents a flow dimension of the respective node;

calculating flow capacity of each node based on the flow dimension, wherein the flow capacity of each node represents the number of connections to a particular node versus the distance or number of node interconnections required to access said particular node from all other nodes of the network; and

ranking each node according to its respective flow capacity.

2. The method of claim 1, wherein each element of the representation matrix uses the number “

1”

to represent the presence of a connection between each of the interconnecting nodes and the number “

0”

to represent the absence of a connection between each of the interconnecting nodes.

3. The method of claim 1, wherein the flow capacity of each node is calculated by equation 1:

$\begin{array}{cc}\mathrm{FC}<br><br>\left(v_i\right)=\frac{1}{\left(n-1\right)}<br><br>\underset{k=1}{\overset{l}{\sum <br><br>}}<br><br>\underset{j=1}{\overset{n}{\sum <br><br>}}<br><br>\frac{k}{d_k<br><br>\left(i,j\right)}& \left(1\right)\end{array}$

wherein

n is the total number of nodes in the network;

i and j denotes particular node i and node j in the network;

l is the highest number in the flow matrix;

d_k(i,j) is the shortest distance from node i to node j in a flow graph representing the flow matrix; and

k is the dimension from 1 to l.

4. The method of claim 1, wherein the representation matrix is provided in upper triangular form.

5. The method of claim 1, wherein all of the elements in the lower diagonal portion of the flow matrix are set to zero such that the flow matrix is in upper diagonal form.

6. The method of claim 1, wherein the network is the internet, and each node is a web page.

7. An apparatus for ranking a node within a network of a plurality of interconnected nodes, each node having a connection to at least one of other nodes in the network, the apparatus including a processor and an algorithm operating according to the steps of:

constructing a representation matrix, wherein each element of the representation matrix represents the connection between each of the interconnected nodes;

obtaining a flow matrix by multiplying the representation matrix by itself, wherein each element of the flow matrix represents a flow dimension of the respective node;

calculating flow capacity of each node based on the flow dimension, wherein the flow capacity of each node represents the number of connections to a particular node versus distances or number of node interconnections required to access said particular node from all other nodes; and

ranking each node according to its respective flow capacity.

8. The apparatus of claim 7, wherein each element of the representation matrix uses the number “

1”

to represent the presence of a connection between each of the interconnecting nodes and the number “

0”

to represent the absence of a connection between each of the interconnecting nodes.

9. The apparatus of claim 7, wherein the flow capacity of each node is calculated by equation 1:

$\begin{array}{cc}\mathrm{FC}<br><br>\left(v_i\right)=\frac{1}{\left(n-1\right)}<br><br>\underset{k=1}{\overset{l}{\sum <br><br>}}<br><br>\underset{j=1}{\overset{n}{\sum <br><br>}}<br><br>\frac{k}{d_k<br><br>\left(i,j\right)}& \left(1\right)\end{array}$

wherein

n is the total number of nodes in the network;

i and j denotes particular node i and node j in the network;

l is the highest number in the flow matrix;

d_k(i,j) is the shortest distance from node i to node j in a flow graph representing the flow matrix; and

k is the dimension from 1 to l.

10. The apparatus of claim 7, wherein the representation matrix is provided in upper triangular form.

11. The apparatus of claim 7, wherein all of the elements in the lower diagonal portion of the flow matrix are set to zero such that the flow matrix is in upper diagonal form.

12. The apparatus of claim 7, wherein the network is the internet, and each node is a web page.