Latent Geometry for Complementarity-Driven Networks

Networks of interdisciplinary teams, biological interactions as well as food webs are examples of networks that are shaped by complementarity principles: connections in these networks are preferentially established between nodes with complementary properties. We propose a geometric framework for complementarity-driven networks. In doing so we first argue that traditional geometric representations, e.g., embeddings of networks into latent metric spaces, are not applicable to complementarity-driven networks due to the contradiction between the triangle inequality in latent metric spaces and the non-transitivity of complementarity. We then propose the cross-geometric representation for these complementarity-driven networks and demonstrate that this representation (i) follows naturally from the complementarity rule, (ii) is consistent with the metric property of the latent space, (iii) reproduces structural properties of real complementarity-driven networks, if the latent space is the hyperbolic disk, and (iv) allows for prediction of missing links in complementarity-driven networks with accuracy surpassing existing similarity-based methods. The proposed framework challenges social network analysis intuition and tools that are routinely applied to complementarity-driven networks and offers new avenues towards descriptive and prescriptive analysis of systems in science of science and biomedicine

Reconstructing networks

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, the authors focus on the inference methods rooted in statistical physics and information theory. The discussion is organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections

Reconstructing networks

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, we shall focus on the inference methods rooted in statistical physics and information theory. The discussion will be organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections.Comment: 107 pages, 25 figure