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.

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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.

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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.

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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.@en

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.

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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.

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As a result of the climate change the situation in Arctic area leads to several important consequences. On the one hand, fossil fuels can be exploited much easier than before. On the other hand, their excavation leads to serious potential threats to fishing by changing natural habitats which in turn creates serious damage to the countries’ economies. Another set of problems arises due to the extension of navigable season for shipping routes. Thus, there are already discussions on how should resources be allocated among countries. In Aleskerov and Victorova (An analysis of potential conflict zones in the Arctic Region, HSE Publishing House, Moscow, 2015) a model was presented analyzing preferences of the countries interested in natural resources and revealing potential conflicts among them. We present several areas allocation models based on different preferences over resources among interested countries. As a result, we constructed several allocations where areas are assigned to countries with respect to the distance or the total interest, or according to the procedure which is counterpart of the Adjusted Winner procedure. We consider this work as an attempt to help decision-making authorities in their complex work on adjusting preferences and conducting negotiations in the Arctic zone. We would like to emphasize that these models can be easily extended to larger number of parameters, to the case when some areas for some reasons should be excluded from consideration, to the case with ‘weighted’ preferences with respect to some parameters. And we strongly believe that such models and evaluations based on them can be helpful for the process of corresponding decision making.

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We propose a model that evaluates how much a network has changed over time in terms of its structure and a set of central elements. The difference of structure is evaluated in terms of node-to-node influence using known nodes correspondence models. To analyze the changes in nodes centralities we adapt an idea of interval orders to the network theory. Our approach can be used to investigate dynamic changes in temporal networks and to identify suspicious or abnormal effects in terms of the topology and its critical members. We can also transform the stability measure to the similarity measure in order to cluster the network in some homogeneous periods. To test our model, we consider the international migration network from 1970 to 2015 and attempt to analyze main changes in migration patterns.

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The Arctic region is one of the most sensitive and vulnerable to climate change. The dramatic melting of Arctic ice has several negative consequences for the whole ecosystem as well as for a way of life of native people but it also creates new opportunities for the region. First, it opens up potential for exploitation of large deposits of natural resources such oil and gas. Second, it shrinks Arctic shipping routes which offer significant economic savings for many countries. These benefits has already attracted many countries, both Arctic and non-Arctic, thus resulting in potential conflict of interests. In our paper we present a mathematical approach to the problem of conflict resolution in the Arctic. First, we propose an approach how the level of interest in each part of the region should be evaluated with respect to main resources - oil, gas, fish and maritime routes. Second, we present several models of areas allocation to resolve the problem of conflict resolution. As a result, we applied several scenarios of areas allocation, evaluated their efficiency based on the total satisfaction level and identified conflict zones in the Arctic.

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Using network approach, we propose a new method of identifying key food exporters based on the long-range (LRIC) and short-range interaction indices (SRIC). These indices allow to detect several groups of economies with direct as well as indirect influence on the routes of different levels in the food network.

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We consider an application of power indices, which take into account preferences of agents for coalition formation proposed for an analysis of power distribution in elected bodies to reveal most powerful (central) nodes in networks. These indices take into account the parameters of the nodes in networks, a possibility of group influence from the subset of nodes to single nodes, and intensity of short and long interactions among the nodes.

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Our study employs the network approach to the problem of international migration. During the last years, migration has attracted a lot of attention and has been examined from many points of view. However, very few studies considered it from the network perspective. The international migration can be represented as a network (or weighted directed graph) where the nodes correspond to countries and the edges correspond to migration flows. The main focus of our study is to reveal a set of critical or central elements in the network. To do it, we calculated different existing and new centrality measures. In our research the United Nations International Migration Flows Database (version 2015) was used. As a result, we obtained information on critical elements for the migration process in 2013.

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The problem of quick detection of central nodes in large networks is studied. There are many measures that allow to evaluate a topological importance of nodes of the network. Unfortunately, most of them cannot be applied to large networks due to their high computational complexity. However, if we narrow the initial network and apply these centrality measures to the sparse network, it is possible that the obtained set of central nodes will be similar to the set of central nodes in large networks. If these sets are similar, the centrality measures with a high computational complexity can be used for central nodes detection in large networks. To check the idea, several random networks were generated and different techniques of network reduction were considered. We also adapted some rules from social choice theory for the key nodes detection. As a result, we show how the initial network should be narrowed in order to apply centrality measures with a high computational complexity and maintain the set of key nodes of a large network.

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Over the last few decades, performance-based funding models of universities have been introduced and have made universities build and implement different strategies to enable them to compete and be viable in changing circumstances. In turn, national governments are focused on providing universities with more opportunities to run efficient programmes that advance higher education. This paper includes a detailed review of various taxonomies for structuring university. More importantly, it develops a typology of higher education institutions that is relevant for the Russian context. The Ward method is used to cluster universities on the basis of university distinctions in terms of the availability of resources, education, and research and development. This typology of universities is verified by assessing their efficiency score gained from modified Data Envelopment Analysis, incorporating universities' heterogeneity. Finally, the paper gives a decision tree for classifying universities bearing in mind their diversity. It might be expanded for a broader set of inputs and outputs, namely external projectbased research funding modes and cooperation between universities and industry to pursue the development of innovation. The results can be used for shaping targeted policies aimed at particular university groups.

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The work is related to the detection of key international and Russian economic journals in cross-citation networks. A list of international journals and information on their cross-citations were taken from Web of Science (WoS) database while information on Russian journals was taken from Russian Science Citation Index (RSCI). We calculated classical centrality measures, which are used for key elements detection in networks, and proposed new indices based on short-range and long-range interactions. A distinct feature of the proposed methods is that they consider individual attributes of each journal and take into account only the most significant links between them. An analysis of 100 main international and 29 Russian economic journals was conducted. As a result, we detected journals with large number of citations to important journals and also journals where the observed rate of self-citation is a dominant in the total level of citation. The obtained results can be used as a guidance for researchers planning to publish a new paper and as a measure of importance of scientific journals.@en

Over the past decades due to increasing economic pressure and rising demands by government and society, the organizational landscape of higher education is changing while university activities become more diversified. The focus of public support is shifting from funding current activities of universities towards rewarding outcomes. There are, as a result, many strategies to adapt and develop universities in this changing environment. For example, emerging typologies for structuring a network of higher education institutions (HEIs) taking into account their diversity are at the forefront in many countries of agendas for greater efficiency in higher education. We advance a typology for HEIs in Russia taking into account indicators of research and teaching activities. We present an overview of best practices for HEIs, some typologies, a set of indicators and mathematical tools for constructing a typology of Russian public HEIs. This typology is based on clustering the input (resource allocation) and output (performance) indicators that characterize academic and educational achievements of HEIs. The proposed classification differentiates types of universities and contains a decision tree that allows assigning universities to one category or another. It can be used as a basis for a comprehensive analysis of diverse Russian universities and for government policies to address each of the identified HEI types, depending on their characteristics.

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The paper examines a choice problem in case of large number of alternatives characterized by a set of criteria. Very often existing choice procedures cannot be used due to their computational complexity. In contrast, the approach proposed in this paper utilizes a set of easy to use techniques having complexity less than the quadratic. We apply super-threshold procedures sequentially in order to find the best alternatives. The application to learning to rank problem is also considered. Finally, two methods of defining thresholds and order of criteria in super-threshold procedures are studied. While the first method is based on the etalon criterion, the second method uses the distribution function. Both methods developed are mainly oriented on the choice of search results in search engines and capable of processing large amount of data in networks, but can also be applied to any system in which the alternatives are represented by a set of criteria.

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