Popularity versus Similarity in Growing Networks

Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks, or duplication. Here we show that popularity is just one dimension of attractiveness. Another dimension is similarity. We develop a framework where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon

A hierarchical Bayesian model for predicting ecological interactions using scaled evolutionary relationships

Identifying undocumented or potential future interactions among species is a challenge facing modern ecologists. Recent link prediction methods rely on trait data, however large species interaction databases are typically sparse and covariates are limited to only a fraction of species. On the other hand, evolutionary relationships, encoded as phylogenetic trees, can act as proxies for underlying traits and historical patterns of parasite sharing among hosts. We show that using a network-based conditional model, phylogenetic information provides strong predictive power in a recently published global database of host-parasite interactions. By scaling the phylogeny using an evolutionary model, our method allows for biological interpretation often missing from latent variable models. To further improve on the phylogeny-only model, we combine a hierarchical Bayesian latent score framework for bipartite graphs that accounts for the number of interactions per species with the host dependence informed by phylogeny. Combining the two information sources yields significant improvement in predictive accuracy over each of the submodels alone. As many interaction networks are constructed from presence-only data, we extend the model by integrating a correction mechanism for missing interactions, which proves valuable in reducing uncertainty in unobserved interactions.Comment: To appear in the Annals of Applied Statistic

A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

The hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The Popularity-Similarity-Optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, reproducing strong clustering and scale-free degree distribution, however it misses to reproduce an important feature of real complex networks, which is the community organization. The Geometrical-Preferential-Attachment (GPA) model was recently developed to confer to the PSO also a community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model that, differently from GPA, forces heterogeneous angular node attractiveness by sampling the angular coordinates from a tailored nonuniform probability distribution, for instance a mixture of Gaussians. The nPSO differs from GPA in other three aspects: it allows to explicitly fix the number and size of communities; it allows to tune their mixing property through the network temperature; it is efficient to generate networks with high clustering. After several tests we propose the nPSO as a valid and efficient model to generate networks with communities in the hyperbolic space, which can be adopted as a realistic benchmark for different tasks such as community detection and link prediction

Recommender Systems

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.Comment: 97 pages, 20 figures (To appear in Physics Reports