Modeling Real Networks with Deterministic Preferential Attachment

Most of real networks show a structure that can be represented quite well by means of growth and probabilistic preferential attachment, leading to optimal features, such as high clustering or scale-freeness. Real networks, however, are not the result of a global optimization strategy; indeed it is more realistic to let new nodes selfishly chose to connect to the existing nodes that maximize their utility, regardless of the global optimality of the resulting network. On the other hand real networks exist and deploy in metric spaces; spatial network models are characterized by some properties because the generated nodes are discarded if they do not comply with some criteria (e.g., too far from existing nodes), while in real situations the arise of a new node in a given position can not be neglected. In this paper a model for the representation of such net works is provided, considering spatial and degree based utility functions, as well as their combination. While the nodes are generated randomly, the preferential attachment strategy is deterministic, and is univocally determined, given the sequence of nodes and the utility to be maximized. The proposed model, although created according to the immediate benefit of nodes, shows some of the properties that can be obtained with global optimization strategies based on probability. A possible application of the proposed model is a linking strategy for a set of distributed dynamic agents (e.g., mobile robots embedded in a space) based on the single agents' perspective, which ensures the connectedness of the resulting network (while other spatial network models give no guarantee), as well as some desirable properties such as reduced total edge length that may minimize the communication time and small diameter, that influences convergence.