Влияние в сетевых структурах с использованием индексов дальних взаимодействий
An axiomatics of power indices in voting with quota was proposed. It relies on the additivity and dictator axioms. Established was an important property that the player’s power index is representable as the sum of contributions of the coalitions in which it is a pivot member. The coalition contributions are independent of the players’ weights or the quota. The general theorem of power index representation and the theorem of representation for a power index of anonymous players were formulated and proved.
The problem of link prediction gathered a lot of attention in the last few years, arising in dierent applications ranging from recommendation systems to social networks. In this paper, we will describe the most popular similarity indices, compare their performance in their ability to show links with the highest probability of being removed from initial network and describe the approach that allows to use them to predict missing links using supervised machine learning. We will show the accuracy of prediction of this method on examples of real networks.
The problem of evaluation of the real power of players when they make collective decisions is considered. The new model of the real power evaluation is proposed. The basics of the new model are: modification of the classical power Shapley - Shubik index for accounting of possibility of coalition formation, adding of the new index of the position of coincidence which is evaluating the closeness of the political position of groups and faction, and the new developed index of power efficiency. The index of power efficiency shows to what extend the players exercised their potential power which depends on the number of their votes. Besides, a new way of accounting the impact of cohesion of groups and factions in their final power score is proposed. This model is applied for the evaluation of the power distribution at the Russian State Duma of the 3d convocation.
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 selfcitation 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.