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. Using the contact process model within a Monte Carlo numerical simulation approach, we mimic an epidemic spreading on a homophilic network, a scale-free network displaying a small world effect, to show a continuous phase transition to an absorbing-state at a critical threshold . Since the connection number k of the vertices’ homophilic network is cumulative, the degree distribution exhibits, for a large value of networks, a power-law behavior according to , with the distribution exponent . A finite-size scaling analysis allows us to characterize the transition by a set of critical exponents , , β and , whose universality class indicates a disagreement with those associated to the CP on scale-free networks in terms of the heterogeneous mean-field theory.

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We propose a simple network growth process where the preferential attachment contains two essential parameters: homophily, namely, the tendency of sites to link with similar ones, and the number of attaching neighbors. It jointly generalizes the Barab asi-Albert model and the scalefree homophilic model with a control parameter which tunes the importance of the homophily on preferential attachment process. Our results support a detailed discussion about di®erent kinds of correlation, in special a¯tness correlation introduced in this paper, and comparisons between BA model, scale-free homophilic model, and our present model considering its topological properties: degree distribution, time dependence of the connectivity and clustering coe±cient.

The spreading of epidemics in complex networks has been a subject of renewed interest of several scientific branches. In this regard, we have focused our attention on the study of the susceptible–infected–susceptible (SIS) model, within a Monte Carlo numerical simulation approach, representing the spreading of epidemics in a clustered homophilic network. The competition between infection and recovery that drives the system either to an absorbing or to an active phase is analyzed. We estimate the static critical exponents , and , through finite-size scaling (FSS) analysis of the order parameter and its fluctuations, showing that they differ from those associated with the contact process on a scale-free network, as well as those predicted by the heterogeneous mean-field theory.