The construction of complex networks is of great importance for the study of agent-based models and dynamical systems, such as opinion models, epidemics, oscillator systems or coupled maps, etc., that use graphs as a substrate to represent the interaction paths. The dynamics can strongly depend on the topological characteristics of the interaction network, therefore, it is essential to build networks with well-defined structural properties. One of the properties of great importance is the average degree, the first moment of degree distribution. In cases where the degree distribution decays like a power law, its exponent is another relevant quantity, related to the possibility of hubs. Within this framework, we study the effects that certain characteristics of the degree distribution have on the properties of the network, built using the configuration model. For each value of the power-law exponent, we fix the minimum, maximum, and average degrees, comparing the effect of these parameters on the resulting networks, through the clustering coefficient and the degree-degree correlation between neighboring sites.