Estimating topological properties of weighted networks from limited information

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks. Prior studies usually focus on the structure-based estimation to infer network sizes, degree distributions, average degrees, and more. Little effort attempted to estimate the specific degree of each vertex from a sampled induced graph, whi...

Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In this work, graph metrics are used in network estimation by developing optimisation methods that incorporate prior knowledge of a network's topology. The derivatives of graph metrics are used in gradient descent schemes for weighted undirec...

Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in empirical network science is how to make the best possible estimates of network structure given such unreliable data. In this paper we describe a fully Bayesian method for reconstructing networks from observational data in any format, even when th...

When a network is reconstructed from data, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the vertex degree distribution of the true underlying network is analytically reconstructed using an iterative procedure. Such procedure is based on the inferred network and estimates for the probabilities $\alpha$ and $\beta$ of type I and type II errors, respectively. The iteration procedure consists of cho...

Network analysis is currently used in a myriad of contexts: from identifying potential drug targets to predicting the spread of epidemics and designing vaccination strategies, and from finding friends to uncovering criminal activity. Despite the promise of the network approach, the reliability of network data is a source of great concern in all fields where complex networks are studied. Here, we present a general mathematical and computational framework to deal with the probl...

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 ...

In this article the problem of reconstructing the pattern of connection between agents from partial empirical data in a macro-economic model is addressed, given a set of behavioral equations. This systemic point of view puts the focus on distributional and network effects, rather than time-dependence. Using the theory of complex networks we compare several models to reconstruct both the topology and the flows of money of the different types of monetary transactions, while imp...

Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very network of connections between agents. The different interlinkages patterns that agents establish may, in fact, lead to asymmetries in the knowledge of the network structure; since this entails a different ability of quantifying relevant systemic properties (e.g. the risk of financial contagion in a network of liabilities), agents capable of...

The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these t...

Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to biological networks and social networks. The data produced by these experiments are often rich and multimodal, yet at the same time they may contain substantial measurement error. In practice, this means that the true network structure can dif...