  Community structures have been identified in various complex real-world
networks, for example, communication, information, internet and shareholder
networks. The scaling of community size distribution indicates the
heterogeneity in the topological structures of the network. The current network
generating or growing models can reproduce some properties, including degree
distributions, large clustering coefficients and communities. However, the
scaling behaviour of the community size lacks investigation, especially from
the perspectives of local interactions. Based on the assumption that
heterogeneous nodes behave differently and result in different topological
positions of the networks, we propose a model of designed random walks in
directed networks to explain the features in the observed networks. The model
highlights that two different dynamics can mimic the local interactions, and a
hidden layer is essential when reproducing the characteristics of real complex
networks. The key features the model can explain include community size
distribution, degree distribution, percolation properties, distribution of
average path length and dependence of the above properties on the labels of
nodes in the data.
