Complex Networks with External Degree

The evolvement of complex networks is based on self-contained ultra-large system, but in fact all possible described networks are almost not completeness sub-networks. We study the more complete information description of complex system through introducing autonomous system and external degree, and investigate the statistical properties of external edges. The external nodes, external edges, and external degree provide natural and powerful extension for the traditional network concept of complex physical system, capable of providing more comprehensive information about the connectivity properties of the graph topology. Complex network with external degree provides scalable scale analysis for complex system with as less cost as possible. Experiments reveal that external degree also follows power-law distribution.