The adoption of a new technology, the spreading of ideologies, the transmission of contagions, are examples of spreading phenomena that can be modelled at two distinct levels of resolution, a macroscopic and a microscopic level. In the present work, we consider the network at the microscopic level and represent its nodes as a system of interacting particles and propose a novel, physics-inspired approach. This approach assumes that nodes interact via 'forces' that derive from the 'potential' that each node creates at the location of the other nodes, leading to a potential gradient that indicates the 'natural' direction of diffusion through the network. A set of influencers in the network, is determined from strategically selected nodes based on the value of their net potential. We use synthetic networks of various sizes and compare the influence spread resulting from a seed set determined from the potential-based model and alternate approaches, including the greedy algorithm of Kempe et al. Our findings indicate that this approach achieves comparable results to those of the greedy algorithm without the prohibitive computational cost, and consistently outperforms the other approaches by a large margin. We then apply our methodology to information spreading related to the Twitter Higgs Boson user dataset. The results are analyzed in the context of influence maximization, and we provide insights into the general application of this technique for information dissemination.
The unveiling of communities within a network or graph, and the hierarchization of its members that results is of utmost importance in areas ranging from social to biochemical networks, from electronic circuits to cybersecurity. We present a statistical mechanics approach that uses a normalized Gaussian function which captures the impact of a node within its neighborhood and leads to a density-ranking of nodes by considering the distance between nodes as punishment. A hill-climbing procedure is applied to determine the density attractors and identify the unique parent (leader) of each member as well as the group leader. This organization of the nodes results in a tree-like network with multiple clusters, the community tree. The method is tested using synthetic networks generated by the LFR benchmarking algorithm for network sizes between 500 and 30,000 nodes and mixing parameter between 0.1 and 0.9. Our results show a reasonable agreement with the LFR results for low to medium values of the mixing parameter and indicate a very mild dependence on the size of the network.
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