Dynamic Network Discovery Stable Community

In the real world, many complex networks exist, and in the most complex networks, there are usually some individuals between whom relationships are denser than those between other individuals and the individuals whose relationships are much relatively denser than others can be classified into a sub-structure of communities. Finding the community in the complex community has an important value, it can help us to understand and develop these networks more effectively.Most of complex networks often changes over time, which is the formation of a prototype of a dynamic network. In this process of change, there will be some community structures that have not change much,which are called stable communities. In this paper, the stable communities are defined as community structure, the number of which appears in the n time slices is larger than a threshold value. Stable community often represent the basic framework of the network, in fact changing network is an extension of a stable community. Network expansion is carried out around the stable community, such as increasing nodes and increasing edges, which have a certain relationship with stable community. In a dynamic network,obtaining the hierarchy of the stable community is very important. Because they make us know the establishment of stable communities.Combining stable community and the dynamic characteristics of networks can solve many practical problems, such as in the shopping system, we can get some contact is fixed by observing a period of time, in fact the community of the people is a form of stable community, which have little change with the change of time. If you want to recommend some products to this system, the stable community will be the first.Discovering community in the dynamic network has great challenges.In existing algorithm, there are two ways. One is that we can merger all of the static network in n time slices into the only one static network, then discover community in the only one static network, the community is called stable community. This method ignore structural characters in some static network, so affect the correctness of the results. The other is that we can discover the static network each time slice, then compare the result of each time slice(such as the intersection operator)to get the structure. The final result is a stable community. This method has a relatively large time complexity. Above two methods can get stable community, but can not get the hierarchy of the community.In this paper,I propose a algorithm to get the stable community and the hierarchy of it for the above shortcomings. The main work of this paper are as follows: In this paper,I use the second thought,which divide the dynamic network into n static network, and discovery community in n static network. In order to get the correct community structure, this paper use GN algorithm. The reason to use it is that it has a relatively high correct rate by comparing with other algorithms. In order to get a stable community, this paper propose a" frequent node set", frequent node set is a collection of all the nodes in the n time slices simultaneously within the same community and a time slice ratio of the numbern is greater than a preset threshold value. Stable community consists of nodes and edges,so we can get the node set of stable community and the hierarchy of the stable community by this way.In the paper, we use a dynamic network test data sets to verify the accuracy and effectiveness of the community division,as well as the introduction of the concept of time slice and frequent node sets, we use them to achieve the division of stale community of the dynamic network.This paper is a contribution that when we get the stable community,we can get the hierarchy of the stable community.