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.
When facing complex mesoscale network structures, it is generally believed that (null) models encoding the modular organization of nodes must be employed. The present paper focuses on two block structures that characterize the mesoscale organization of many real-world networks, i.e. the bow-tie and the core-periphery ones. Our analysis shows that constraining the network degree sequence is often enough to reproduce such structures, as confirmed by model selection criteria as AIC or BIC. As a byproduct, our paper enriches the toolbox for the analysis of bipartite networks - still far from being…
To understand, predict, and control complex networked systems, a prerequisite is to reconstruct the network structure from observable data. Despite recent progress in network reconstruction, binary-state dynamics that are ubiquitous in nature, technology and society still present an outstanding challenge in this field. Here we offer a framework for reconstructing complex networks with binary-state dynamics by developing a universal data-based linearization approach that is applicable to systems with linear, nonlinear, discontinuous, or stochastic dynamics governed by monotonous functions. The …
Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is tough. Conventional methods focus on either network structure inference task or dynamics reconstruction problem, very few of them can work well on both. This paper proposes a universal framework for reconstructing network structure and node dynamics at the same time from observed time-series data of nodes. We use a differentiable Bernoulli sampling process …
In this paper, we propose a general framework for optimal control measures, which follows the evolution of COVID-19 infection counts collected by Surveillance Units on a country level. We employ an autoregressive model that allows to decompose the mean number of infections into three components that describe: intra-locality infections, inter-locality infections, and infections from other sources such as travelers arriving to a country from abroad. We identify the inter-locality term as a time-evolving network and when it drives the dynamics of the disease we focus on its properties. Tools from…
Faculty of Information Studies in Novo Mesto（新梅斯托信息研究学院）；Universitat Pompeu Fabra（庞培法布拉大学）；Jožef Stefan Institute（约瑟夫·斯特凡研究所）；University of Ljubljana（卢布尔雅那大学）
Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two indepen…
Population mobility can be studied readily and cheaply using cellphone data, since people's mobility can be approximately mapped into tower-mobile registries. We model people moving in a grid-like city, where edges of the grid are weighted and paths are chosen according to overall weights between origin and destination. Cellphone users leave sparse signals in random nodes of the grid as they move by, mimicking the type of data collected from the tower-cellphone interactions. From this noisy data we seek to build a model of the city, {\it i.e.} to predict probabilities of paths from origin to d…
Reconstructing MSM Sexual Networks to Guide PrEP Distribution Strategies for HIV Prevention
BRAN Lab, Network Science Institute, Northeastern University London（英国东北大学伦敦分校网络科学研究所）；Kent Medway Medical School（肯特梅德韦医学院）；Network Science Institute, Northeastern University（美国东北大学网络科学研究所）；Department of Mathematics, Northeastern University（美国东北大学数学系）；INESC-ID, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院计算科学与工程研究所）；LASIGE, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院LASIGE实验室）
研究通过重建MSM性网络，发现网络结构对HIV传播模拟结果有显著影响，基于度或k壳中心性针对性PrEP策略在 assortative by age和race网络中效果最佳，但数据驱动的PrEP分配在 assortative by age和race网络中表现欠佳。
Reconstructing temporal multi-relational firm networks at scale using large language models. The case of the semiconductor industry
Supply Chain Intelligence Institute Austria (ASCII)（奥地利供应链情报研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；Medical University of Vienna, Section for Science of Complex Systems, CeMSIIS（维也纳医科大学复杂系统科学系，CeMSIIS）；Smith School of Enterprise and Environment, University of Oxford（牛津大学史密斯企业与环境学院）；Institute of New Economic Thinking, University of Oxford（牛津大学新经济思维研究所）
ETH Z\"urich, Chair of Systems Design Weinbergstrasse 56/58, Z\"urich, Switzerland
Positive and negative relations play an essential role in human behavior and shape the communities we live in. Despite their importance, data about signed relations is rare and commonly gathered through surveys. Interaction data is more abundant, for instance, in the form of proximity or communication data. So far, though, it could not be utilized to detect signed relations. In this paper, we show how the underlying signed relations can be extracted with such data. Employing a statistical network approach, we construct networks of signed relations in four communities. We then show that these r…
Recent crises have shown that the knowledge of the structure of input-output networks at the firm level is crucial when studying economic resilience from the microscopic point of view of firms that rewire their connections under supply and demand shocks. Unfortunately, empirical inter-firm network data are rarely accessible and protected by confidentiality. The available methods of network reconstruction from partial information, which have been devised for financial exposures, are inadequate for inter-firm relationships because they treat all pairs of nodes as potentially interacting, thereby…
Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for prediction, optimization, and control of diffusion dynamics. Unfortunately, in most cases the transmission rates are unknown and need to be reconstructed from the spreading data. Moreover, in realistic settings it is impossible to monitor the state of each node at every time, and thus the data is highly incomplete. We introduce an efficient dynamic message-passing…
University of Sao Paulo（圣保罗大学）；Northwestern University（西北大学）
Human mobility has a significant impact on several layers of society, from infrastructural planning and economics to the spread of diseases and crime. Representing the system as a complex network, in which nodes are assigned to regions (e.g., a city) and links indicate the flow of people between two of them, physics-inspired models have been proposed to quantify the number of people migrating from one city to the other. Despite the advances made by these models, our ability to predict the number of commuters and reconstruct mobility networks remains limited. Here, we propose an alternative app…
