A New Approach of Trust Relationship Measurement Based on Graph Theory

The certainty trust relationship of network node behavior has been presented based on graph theory, and a measurement method of trusted-degree is proposed. Because of the uncertainty of trust relationship, this paper has put forward the random trusted-order and firstly introduces the construction of trust relations space (TRS) based on trusted order. Based on all those above, the paper describes new method and strategy which monitor and measure the node behavior on the expectancy behavior character for trusted compute of the node. According to manifestation of node behavior and historical information, adjust and predict the trusted-order of node behavior. The paper finally establishes dynamic trust evaluation model based node behavior characters, and then it discusses the trusted measurement method which measures the connection and hyperlink for node behavior of network in trust relationship space.


I. INTRODUCTION
In recent years, with the wide application of trusted computing in the network security area, the studies of trust relationship in the node behavior of network have been made an important point [1, 2, and 3].However, conventional environment of trust relationship conduction is "man around the model of experience", which is difficult to deal with the trust featured by procedures of brain thinking.Because of the almighty ability of experience model while processing empiricism information, people depend on experience model to a great extent.When the results from experience model are different from the reality significantly, people will doubt it.This is the reason of the occurrence of the incompatible problems when traditional information of trust relationship conducting ways is applied to process node behavior of network system.
The trust network model is the prerequisite of trusted computing, how to evaluate the trust in the network, there is not a unity and general method up to now.In fact, the trust network is a kind of network with trust relationships, trust relationship networks can be abstracted as a kind of topological relationships in mathematics.Recently, the research around the model of trust networks is come from different angles [1][2][3][4][5][6].But their common point is seeking a formal representation method reasonably.
Studies in literature [3] have shown that a trust relationship can be expressed with a graph.In the paper we study a quantitative expression of trust relationship in network system by using the method of graph theory.Then it measures the trusted degree of each node, and it also presents the trusted measurement of the connection and hyper connection for node behavior of network.
The object of this paper is to establishes dynamic trust evaluation model based on node behavior characters, Through the construction of the relationship between practical node behavior characters and on-the-spot model, it sets up a couple of mapping models of trust relationship, and sketches the skeleton of relationship mapping inversion.
The paper is organized as follows.Section 2 introduces the basic concept of trust relationship based on graph theory, and some properties of the evaluate principle of the trusted network.Section 3 studies measurement of trusted relationship.Section 4 we present dynamic trust evaluation model based on random trusted relationship.Section 5, conclusion puts forward the discoveries of this research and future research direction.

A. Certainty trusted relational graphs
Suppose that a trusted network N T can be expressed as   is an edge set.Moreover, . Therefore, the trusted graph G is called a directed graph.For example, given a trusted network with five vertices, based on the analyzing of network behaviors, the trust relationship of vertices is described as follows:

B. Trusted relational trees
Given a trusted network with five vertices (As shown in Figure 1), Let Based on the graph theory, the trusted path determines the trusted level in trusted networks.The above analysis can be representing by the tree in figure 2.

  K
. In order to ensure the limit convergence, and furthermore, the measuring value of each node should be trusted degree, therefore this paper regard the following limit as the measuring of each node in the trusted relational graph in networks: It will find in fig. 2 that the measurement of the trusted degree about each node is the number of the path in the directed tree, which takes each node for the root.And then the relations are extended to the general case, the definition is as follows: Definition 3.1 In a network with n nodes, the trusted capability (trusted degree) of a node i v can be determining by the number of the path, which connects with the K-th path and starts from the node i v .This number is called the K-th trusted capability, and denoted as is called the K-th trusted capability vector of the trusted relational graph G .Definition 3.2 In a network of n vertices, a limit ( www.ijacsa.thesai.org is entitled relatively limit trusted degree of the node i v , it is called a trusted degree for short.For that reason, we have which is called a trusted vector of each node in the trusted relational graph, where Let G be a trusted relational graph of n vertices, its adjacency matrix is ,  is an eigenvector corresponding to the biggest values of , A then T exists certainly and ) /( It can seem from theorem3.1, the K-th trusted degree ) (k TD of each node is computable in the trusted relational graph G with n vertices, and it can be obtain by the following algorithm: (1)when The algorithm given in theorem3.1 can be put to use in network according to different trusted levels.Regardless of the connected meaning of network note, it always measures the trusted degree in the trusted relational graph.Meanwhile, the trusted vector T can be regaled as a weighted vector, which expresses the trusted degree of each node in the trusted relational graph.

IV. RANDOM TRUSTED RELATIONSHIP
Thinking about the trusted relational graph of discussion in the previous section, if it has , then it exists the trusted relationship of completely specified between i v and j v It is called certainty trusted relational graph which has the trusted relationship of completely specified.In fact, trusted relationship is uncertainty in lots of trusted networks.For example, the trusted relationship among people in the Internet, because of the vitality of network activities, the trusted relationship of network is uncertainty, for this reason, the uncertain research methods is used to analyze the trusted relationship in network.
relational graph G is shown in Figure1.

Figure 2 .
Figure 2. Trusted relational tree III.MEASUREMENT IN TRUSTED RELATIONSHIP The indirect trusted vector of each node in the network (when K=2) is as follows: ( ) 2 (  TD 2，4，7，6，4 transfer probability of a node i v .Based on the probability theory, it is well known that the transfer probability of the path ij L (as dependence), which is from the node i to say it is a probability of the directed connection (trusted relational chain)between the node i of paths, which starting from the node i v and taking with k paths.We can prove as follows: limit transfer probability of each node exists certainly, and equals to the limit www.ijacsa.thesai.org trusted level vector of each node.Such as the number of trusted vectors about the The random trusted relationship is expressed by the random graph for trusted relationship, it has respective trusted relational graph in the basis of different network activities and space-time states.Furthermore, the extent of trusted relationships presents certain probabilistic characteristics with the change of network