Variable Neighborhood Search for extremal vertices : The AutoGraphiX-III system

More than fifteen years after the beginning of the development of AutoGraphiX (AGX), a third version of the software is made available. Since the program was rewritten from scratch, it was the opportunity to look forward and consider new avenues. From the user׳s point of view, the interface is completely changed, which allows the display of multiple information which was not possible in the previous versions. However, one of the main improvements is that it is designed to help researchers in the field of complex networks. In these days when increasing research is applied to complex networks (such as social networks), the use of quantities related to vertices, indicating the centrality (the importance of an actor in the network measured as a topological indicator) naturally leads researchers toward the mathematical study of these quantities. This new paradigm implies a complete change in the optimization algorithm that now natively handles multi objective optimization problems involving vertex-related measures.