Analytical approach to the Axelrod model based on similarity vectors

Complex problems of social interaction are usually studied within the framework agent-based models. Some these problems, such as issue alignment and opinion polarization, better suited in $n$-dimensional space. Although this kind complex problem may be explored by numerical simulations, simulations can hinder our ability to obtain general results. In work, we show how, under certain conditions, a classical multidimensional model Axelrod give rise closed set master equations terms vector similarities between agents. The analytical results fully agree with on complete networks, accurately predict similarity distribution whole system sparse topologies, provide good approximation physical links that improves when mean degree increases.