Networks/Theory VI

We compare two versions of the nonlinear q-voter model: the original one, with annealed randomness, and the modified one, with quenched randomness. In the original model, each voter changes its opinion with certain probability ε if the group of influence is not unanimous. In contrast, the modified version introduces two types of voters that act in a deterministic way in case of disagreement in the influence group: the fraction ε of voters always change their current opinion, whereas the rest of them always maintain it.

Experimentally observed complex networks often simultaneously exhibit scale-free degree distribution, small-world property and high clusterization. Classical textbook models of network theory (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz, geometrical random graphs in Euclidean space, etc.) cannot simultaneously reproduce all three of these properties. It has been known at least since [1] that geometrical random graphs on a hyperbolic disk can reproduce all three and are therefore a good candidate model for understanding the structure of experimentally observed datasets.

Link prediction is a common problem that allow us to know missing links in a complex networks, unknown preferences of a user who wants that someone recommends him a movie, what a politician will vote… In our work we focus on mix-membership stochastic block models to predict links in bipartite networks [1] but adding node’s metadata like an user’s age, a movie’s genre, a politician’s state...

Networks provide useful tools for analyzing diverse complex systems from natural, social, and technological domains. Growing size and variety of data such as more nodes and links and associated weights, directions, and signs can provide accessory information. Link and weight abundance, on the other hand, results in denser networks with noisy, insignificant, or otherwise redundant data. Moreover, typical network analysis and visualization techniques presuppose sparsity and are not appropriate or scalable for dense and weighted networks.