Reliability Of Complex Networks

The complex network reliability research is extremely important to understand the network's topology and behavior.There exists close correlation between the topology in real networks and reliability research.And the reliability for different networks is different. It's been shown that different network topology has different reliability.Especially, scale free network is more robust than ER random network when facing random failure,while the former is much more vulnerable than the latter when attack.However,since we understand very little about the complex network topology, even has very big deviation, the complex network reliability research is always a very difficult question.At present complex network reliable research mostly concentrates to the influence that attack pattern play on to network topology.Attack based on degree and between-ness is researched extensively because they can reflect the importance of the nodes to some extent.However, all these studies are about the dynamic structure behavior changing with the geometry measure after complex networks attacked,there is no definite macroscopic quantity measuring the complex network reliability. This is also precisely our goal.First,in this paper,the macroscopic research about complex network reliability is studied,and a measure for complex networks is proposed. Next, the algorithm computing complex network connecting probability is given.Through simulating and analyzing about connecting probability after attack in different network models,we find that: 1st, along with network scale increasing, connecting probability assumes the linear growth tendency; 2nd, network connection probability compositor is: BA>ER>Random□networks≈WS when failure ;while ER> Random □networks≈WS>BA when intentional attackThe theory and the practice all proved that, complex network connecting probability not only portrayed the complex network reliability, but also expressed the complex network reliability with the accurate quantity.Finally, a static parameter measuring network frangibility—toughness is given,which may be very good way to measure the network reliability and the vulnerability if combining with connecting probability.