Transparency effect in the emergence of monopolies in social networks

Power law degree distribution was shown in many complex networks. However, in most real systems, deviation from power-law behavior is observed in social and economical networks and emergence of giant hubs is obvious in real network structures far from the tail of power law. We propose a model based on the information transparency (transparency means how much the information is obvious to others). This model can explain power structure in societies with nontransparency in information delivery. The emergence of ultra powerful nodes is explained as a direct result of censorship. Based on these assumptions, we define four distinct transparency regions: perfect non-transparent, low transparent, perfect transparent and exaggerated regions. We observe the emergence of some ultra powerful (very high degree) nodes in low transparent networks, in accordance with the economical and social systems. We show that the low transparent networks are more vulnerable to attacks and the controllability of low transparent networks is harder than the others. Also, the ultra powerful nodes in the low transparent networks have a smaller mean length and higher clustering coefficients than the other regions.