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