The Researches On The Invulnerability Of Scale-Free Networks With The Consideration Of Cost

The complex network with characteristics of scale-free property is the scale-free network. The degree distribution of the network meets power-law distribution, namely the probability with self-similarity. The so-called self-similarity refers the function form with similar properties in different form of magnification. The so-called scale invariance refers to the degree distribution network being similar in any scale. We can't find a characteristic of the scale to depict the network of nature.Barabasi put forward the view in nature that the scale-free network in selective attack is fragile, this is the main arguments of the current complex network resistance to offensive research. This argument was thought scale-free network in selective attacks, a few important node or edge has been removed will make the whole network rapid collapse. However, we found that the conclusion exists the inconsistencies with actual network. The Internet is a scale-free network in real-world, the purposes of network design is to resist nuclear strike such selective attack, and under the selective attack such as the virus and hackers etc, it never appears the phenomenon of overall collapse. This shows the fact which is not consistent with the above conclusion that the reality of the Internet is not fragile in selective attack. This paper therefore was studied, and proved that the Scale-free network may not fragile in the circumstances of considering costs, in certain circumstances, it may be the most robust network. Major work as follows:1)Analyze the reality of network, and draw the reason that reality is not consistent with mainstream is the latter assume that cost of attack of all nodes are equal, however , the cost of attack of each node in network may not equal in reality.2)Revise the main arguments, this paper defined attack cost as removed node degree under attack, and defined compactness of network as node degree and related degree of all other nodes importance measure.3) Based on the simulation experiments of five network , we draw the two conclusions: In the case of different cost of attack , scale-free network in selective node attacks may be robust;Further, more compact and the average degrees of scale-free network in selective node attack more robust, and in the conditions of the same average degrees, the more compact structure of the network more robust.This conclusion riches resistance to aggressive theory of scale-free networks, and provides the stability studies for complex structure of network ,then provides an important basis for complex system stability study, it can also be used to establish robust social, creatures and technology network, get drug targets collapse crime group, etcThe main innovation points for this paper:1)Challenging the main argument that the current scale-free network in selective attack is fragile; and point out that the premise of the same nodes attack cost is false, in different premise conditions of attack cost, the scale-free network is not fragile in selective attack.2) In different premise conditions of attack cost, two factors impacting the scale-free network robust are network compactness and network average degree.