Abstract: The k-core decomposition algorithm was applied to the study of the Internet fractal property. During the study， the difference of fitting results between high-core region and low-core region was analyzed， and a conjecture was proposed that Internet fractal is related to its hierarchical structure. Subsequently， the k-core decomposition process was observed from three aspects: the number and ratio of deleted edges， and subnets distribution. A partition boundary was found which was useful to distinguish core and periphery， then the Internet fractal hierarchy was studied with the help of the skeleton theory. Finally， relations between part and whole， part and part were observed from degree distribution exponent， assortativity coefficient， and entropy. The observations show that the subnets in the Internet edge can characterize the network from the statistics above.

Key words: complex networks, Internet, fractal, k-core decomposition, fractal hierarchy