We study human mobility networks through timeseries of contacts between individuals. Our proposed Random Walkers Induced temporal Graph (RWIG) model generates temporal graph sequences based on independent random walkers that traverse an underlying graph in discrete time steps. Co-location of walkers at a given node and time defines an individual-level contact. RWIG is shown to be a realistic model for temporal human contact graphs, which may place RWIG on a same footing as the Erdos-Renyi (ER) and Barabasi-Albert (BA) models for fixed graphs. Moreover, RWIG is analytically feasible: we derive closed form solutions for the probability distribution of contact graphs.

The concept of centrality is one of the essential tools for analyzing complex systems. Over the years, a large number of centrality indices have been proposed that account for different aspects of a network. Unfortunately, most real networks are substantially incomplete, which affects the results of the centrality measures. This article aims to evaluate the sensitivity of 16 centrality measures to the presence of errors or incomplete information about the structure of a complex network. Our experiments are performed across 113 empirical networks. As a result, we identify centrality indices that are highly vulnerable to incomplete data.

Understanding of real systems relies on the identification of its central elements. Over the years, a large number of centrality measures have been proposed to assess the importance of nodes in complex networks. However, most real networks are incomplete and contain incorrect data, resulting in a high sensitivity of centrality indices. In this paper, we examine the robustness of centrality to the presence of errors in the network structure. Our experiments are performed on weighted and unweighted real-world networks ranging from the criminal network to the trade food network. As a result, we discuss a sensitivity of centrality measures to different data imputation techniques.

Abstract: Identification of central elements in networks is an ill-defined problem. Hence, a large number of centrality measures have been proposed in the literature. We present a survey of existing axioms, which characterize certain properties of centralities. We also perform a perturbation analysis of centrality measures in real and artificial networks.

Modelling temporal networks is an open problem that has attracted researchers from a diverse range of fields. Currently, the existing modelling solutions of time-evolving graphs do not allow us to provide an accurate graph sequence. In this paper, we examine the network dynamics from a system identification perspective. We prove that any periodic graph sequence can be accurately modelled as a linear process. We propose two algorithms, called Subspace Graph Generator (SG-gen) and Linear Periodic Graph Generator (LPG-gen), for modelling periodic graph sequences and provide their performance on artificial graph sequences. We further propose a novel model, called Linear Graph Generator (LG-gen), that can be applied to non-periodic graph sequences. Our experiments on artificial and real networks demonstrate that many temporal networks can be accurately approximated by periodic graph sequences.

Tornado prediction methods are analyzed. A model, based on the superposition principle applied for different methods of data analysis has been built. For efficiency evaluation, the constructed model has been tested on real data. It is shown that the constructed tornado prediction model is more efficient than previous models.

The COVID-19 pandemic have changed our lives and caused severe social, economic and environmental disruption worldwide. This paper examines the impact of coronavirus outbreak and subsequent wave of lockdowns and travel restrictions on air transportation from the network perspective. Using the air traffic data from 2019 to 2021, we examine how the structure of the network has changed both globally and locally. We quantify the similarity of air transportation network for adjacent years and compare it to the pre-pandemic period. The connectivity configuration of countries is also considered. Finally, we identify the most important participants of the air transportation industry and reveal countries with the largest change of centrality during the pandemic.

The analysis of networks describing many social, economic, technological, biological and other systems has attracted a lot of attention last decades. Since most of these complex systems evolve over time, there is a need to investigate the changes, which appear in the system, in order to assess the sustainability of the network and to identify stable periods. In the literature, there have been developed a large number of models that measure the similarity among the networks. There also exist some surveys, which consider a limited number of similarity measures and then perform their correlation analysis, discuss their properties or assess their performances on synthetic benchmarks or real networks. The aim of the article is to extend these studies. The article considers 39 graph distance measures and compares them on simple graphs, random graph models and real networks. The author also evaluates the performance of the models in order to identify which of them can be applied to large networks. The results of the study reveal some important aspects of existing similarity models and provide a better understanding of their advantages and disadvantages. The major finding of the work is that many graph similarity measures of different nature are well correlated and that some comprehensive methods are well agreed with simple models. Such information can be used for the choice of appropriate similarity measure as well as for further development of new models for similarity assessment in network structures.

In recent decades, a large number of centrality measures have been proposed to assess the importance of nodes in complex networks. The choice of the most appropriate centrality index for specific applications is one of the biggest challenges. This paper performs the perturbation analysis of 8 centrality measures. Since most real networks are incomplete and prone to bias, we compare centrality measures in order to evaluate their sensitivity to small changes in a graph structure. Our experiments are performed on 8 classical graph structures ranging from a simple path graph to a Watts-Strogatz graph model. As a result, we provide a sensitivity of centrality measures on different graph structures.

Over the last number of years there has been a growing interest in the analysis of complex networks which describe a wide range of real-world systems in nature and society. Identification of the central elements in such networks is one of the key research areas. Solutions to this problem are important for making strategic decisions and studying the behavior of dynamic processes, e.g. epidemic spread. The importance of nodes has been studied using various centrality measures. Generally, it should be considered that most real systems are not homogeneous: nodes may have individual attributes and influence each other in groups while connections between nodes may describe different types of relations. Thus, critical nodes detection is not a straightforward process. New Centrality Measures in Networks presents a class of new centrality measures which take into account individual attributes of nodes, the possibility of group influence and long-range interactions and discusses all their new features. The book provides a wide range of applications of network analysis in several fields - financial networks, international migration, global trade, global food network, arms transfers, networks of terrorist groups, and networks of international journals in economics. Real-world studies of networks indicate that the proposed centrality measures can identify important nodes in different applications. Starting from the basic ideas, the development of the indices and their advantages compared to existing centrality measures are presented.

Tornado prediction variables are analyzed using machine learning and decision analysis techniques. A model based on several choice procedures and the superposition principle is applied for different methods of data analysis. The constructed model has been tested on a database of tornadic events. It is shown that the tornado prediction model developed herein is more efficient than a previous set of machine learning models, opening the way to more accurate decisions.

Since 9/11, terrorism has become a global issue of the twenty-first century. Terrorist organizations become important actors of world politics as they gain influence on political process and decision-making. Some organizations compete with each other in order to gain more power and influence. We study the distribution of power among terrorist groups using network approach and applying classic and new centrality indices (Short-Range (SRIC) and Long-Range interactions indices (LRIC)). These indices allow to identify terrorist groups with direct and indirect influence on the terrorist network.

The paper examines the choice problem when the total number of observations and criteria is too large. There are many different procedures, which are used for decision-making process under multiple criteria; however, most of them cannot be applied to large datasets due to their computational complexity while others provide sufficient accuracy. To solve the problem, we consider the idea of superposition, which consists in the sequential application of choice functions where the result of the previous function is the input for the next function. Among the main benefits of the superposition are its manageable computational complexity and high performance. We analyze normative properties of the superposition that characterize how stable and sensible the final choice is. We also consider the application of superposition to tornado prediction and search problems. As a result, we show that superposition of choice functions provides higher efficiency values compared to traditional solutions.

Using the consolidated banking statistics (CBS) on foreign claims over the period 2005-2020, we examine the relationship between national banking systems from the network perspective. Our main goal is to identify financial communities and systemically important elements and study their evolution. We compare the snapshots of the foreign claims network and analyze how it changes over time for various centrality measures and community structure of the network. As a result, we identify the most important participants of the global financial system, which are the major players with high ratings and positive credit history or intermediary players, which have a great scale of financial activities. Finally, we perform hierarchical clustering of the snapshots to reveal the main changes in the international lending process.

We propose a novel method to estimate the level of interconnectedness of a financial institution or system, as the measures currently suggested in the literature do not fully take into consideration an important aspect of interconnectedness - group interactions of agents. Our approach is based on the power index and centrality analysis and is employed to find a key borrower in a loan market. It has three distinctive features: it considers long-range interactions among agents, agents’ attributes and a possibility of an agent to be affected by a group of other agents. This approach allows us to identify systemically important elements which cannot be detected by classical centrality measures or other indices. The proposed method is employed to analyze the banking foreign claims as of 1Q 2015. Using our approach, we detect two types of key borrowers (a) major players with high ratings and positive credit history; (b) intermediary players, which have a great scale of financial activities through the organization of favorable investment conditions and positive business climate.

As a result of the global warming, the situation in the Barents Sea leads to several important consequences. Firstly, oil and gas drilling becomes much easier than before. Therefore, it may raise the level of discussions on disputed shelf zones where the deposits are located, especially near to Norway-Russia sea border. Secondly, oil and gas excavation leads to potential threats to fishing by changing natural habitats, which in turn can create serious damage to the economies. We construct a model, which helps to highlight potential disputed territories and analyze preferences of the countries interested in fossil fuels and fish resources. We also compare different scenarios of resource allocation with allocation by current agreement.

Power of nodes has been studied in many works, in particular, using centrality concepts. However, in some applications, a large flow between two nodes implies that these nodes become too interdependent on each other. For instance, in trade networks, the possible shortage of flow between two countries may lead to the deficit of goods in the importing country but, on the other hand, it may also affect the financial stability of the exporting country. This feature is not captured by existing centrality measures. Thus, we propose an approach that takes into account interdependence of nodes. First, we evaluate how nodes influence and depend on each other via the same flow based on their individual attributes and a possibility of their group influence. Second, we present several models that transform information about direct influence to a single vector with respect to the network structure. Finally, we compare our models with centrality measures on artificial and real networks.

We consider an application of long-range interaction centrality (LRIC) to the problem of the influence assessment in the global retail food network. Firstly, we reconstruct an initial graph into the graph of directed intensities based on individual node’s characteristics and possibility of the group influence. Secondly, we apply different models of the indirect influence estimation based on simple paths and random walks. This approach can help us to estimate node-to-node influence in networks. Finally, we aggregate node-to-node influence into the influence index. The model is applied to the food trade network based on the World International Trade Solution database. The results obtained for the global trade by different product commodities are compared with classical centrality measures.

Over the past years, there is a deep interest in the analysis of different communities and complex networks. Identification of the most important elements in such networks is one of the main areas of research. However, the heterogeneity of real networks makes the problem both important and problematic. The application of SRIC and LRIC indices can be used to solve the problem since they take into account the individual properties of nodes, the possibility of their group influence, and topological structure of the whole network. However, the computational complexity of such indices needs further consideration. Our main focus is on the performance of SRIC and LRIC indices. We propose several modes on how to decrease the computational complexity of these indices. The runtime comparison of the sequential and parallel computation of the proposed models is also given.

Using the SIPRI Arms Transfers Database covering all trade in military equipment over the period 1950–2018, we examine the relationship between countries from a novel empirical perspective. We consider the arms transfers network as a multiplex network where each layer corresponds to a particular armament category. First, we analyze how different layers overlap and elucidate main ties between countries. Second, we consider different patterns of trade in order to identify countries specializing on particular armament categories and analyze how they change their export structure in dynamic. We also examine how countries influence each other at different layers of multiplex network. Finally, we analyze the influence of countries in the whole network.