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While previous works have shown that an overwhelming number of scale-freenetworks are sparse, there still exist some real-world networks includingsocial networks, urban networks, information networks, which are by observationdense. In this paper, we propose a novel framework for generating scale-freegraphs with dense feature using two simple yet helpful operations, first-ordersubdivision and Line-operation. From the theoretical point of view, our methodcan be used not only to produce desired scale-free graphs with density feature,i.e. power-law exponent $\gamma$ falling into the interval $1<\gamma\leq2$, butalso to establish many other unexpected networked models, for instance,power-law models having large diameter. In addition, the networked modelsgenerated upon our framework show especially assortative structure. That is,their own Pearson correlation coefficients are able to achieve the theoreticalupper bound. Last but not the least, we find the sizes of community in theproposed models to follow power-law in form with respect to modularitymaximization.

Dense networks with scale-free feature