Research On Fractal Properties Of The Internet

As a new research method,the fractal theory has broken the diaphragm between the parts and the whole,and found the medium from part to whole i.e.the similarity between them.The method reveals relations between them in multilevel,multipoint of view and multi-dimension,which may provide a basis that can help people understand the whole from parts,understand the infinite from limited resources.First,problems are founded when applying traditional scaling methods,the burning algorithm and the k-core decomposition algorithm,to the study of the Internet fractal properties.And a conjecture is proposed that the fractal scaling of the Internet has relationships with its hierarchical structure.Second,the statistical features of two opposite processes-"from core to edge" and "from edge to core" is collected and the multilevel-characteristics of the Internet are summarized.Both the collections and summaries help to construct the "core-periphery" segmentation method which can calculate the fractal dimension effectively.Later,the method efficacy is testified and the Internet fractal hierarchy is verified.Last,the segmentation method proposed is used to study the fractal scaling of the Internet.The results shows that the periphery subnets can characterize the Internet in the degree distribution exponent,distribution coefficient and entropy.However,the core of Internet cannot.Furthermore,the periphery subnets can characterize each other in the properties above.In comparison with other methods,the method considers the particularity of the Internet nodes and edges,and maintains the Internet structure properties during the reforming process.They both help to keep the self-similarity of the Internet.The segmentation method can help to get further understanding of the relations between part and whole,to solve the problems caused by the Internet complexity,and to observe the structure in a deeper level.Furthermore,it provides a theoretical guidance for the following research.