Reconstructing topological properties of complex networks using the fitness model

Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of a complex system (e.g. the degree, the clustering coefficient), it is usually necessary to completely reconstruct the network of relations between the subsystems. Several methods are available to detect the existence of interactions between...

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 ...

Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural information hidden in limited amounts of data accompanied by noise and in the presence of inaccessible nodes. Here, we develop a general framework for robust reconstruction of complex networks from sparse and noisy data. Specifically, we dec...

Initially designed to predict and explain the economic trajectories of countries, cities, and regions, economic complexity has been found applicable in diverse contexts such as ecology and chess openings. The success of economic complexity stems from its capacity to assess hidden capabilities within a system indirectly. The existing algorithms for economic complexity operate only when the underlying interaction topology conforms to a bipartite graph. A single link disrupting ...

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...

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of...

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the f...

Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring properties of a network inferred from data, we aim to ask how typical is that network? What properties of the observed network are typical of all such scale free networks, and which are peculiar? To do this we propose a series of methods t...

Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can emerge from the same simple growth dynamics of the node connectivities and of the link weights. A weighted fitness network is introduced in which both nodes and links are assigned intrinsic fitness. This model can show a local dependence o...

Most empirical studies of networks assume that the network data we are given represent a complete and accurate picture of the nodes and edges in the system of interest, but in real-world situations this is rarely the case. More often the data only specify the network structure imperfectly -- like data in essentially every other area of empirical science, network data are prone to measurement error and noise. At the same time, the data may be richer than simple network measure...