Inferring scale-free networks via multiple linear regression and preferential attachment

The problem of reverse-engineering the topology of interaction networks from time-course experimental data has been the subject of a considerable research effort in the last years, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. An important insight into such topic was brought by the introduction of the concept of scale-free topology, whose implications have been widely discussed in literature over the last decade. The aim of this work is to investigate whether it is possible to improve the performances of an inference technique, based on dynamical linear systems and multiple linear regression, by exploiting the same mechanisms that underpin scale-free networks generation, i.e. growth and preferential attachment (PA). The work is prominently concerned with applications in the biological domain, though the algorithm can be in principle adapted also to other frameworks. A statistical evaluation is performed, by using numerically simulated networks, showing that the growth and PA mechanisms actually improve the inference power of the considered technique. Finally the method has been applied to a biological case-study, validating the results against experimental data available in literature.