Ivan Belik

The Analysis of Split Graphs in Social Networks Based on the K-Cardinality Assignment Problem

In terms of social networks, split graphs correspond to the variety of interpersonal and intergroup relations. In this paper we analyse the interaction between the cliques (socially strong and trusty groups) and the independent sets (fragmented and non-connected groups of people) as the basic components of any split graph. Based on the Semi-Lagrangean relaxation for the k-cardinality assignment problem, we show the way of minimizing the socially risky interactions between the cliques and the independent sets within the social network.

Shapley-Based Stackelberg Leadership Formation in Networks

In the given research we study a leadership formation of the most influential nodes in networks. Specifically, we analyze the competition between a leader and a follower based on the Stackelberg leadership model. Applying the concept of Shapley value to measure node’s importance, we represent the mechanism of Shapley-based Stackelberg leadership formation in networks. The approach is tested and represented in tabular and graphical formats.

The Analysis of Leadership Formation in Networks Based on Shapley Value

In the given research we analyse how an agent can move towards leadership in a socio-economic network. For the node’s (i.e., agent’s) importance measure we use the Shapley value (SV) concept from the area of cooperative games. We consider SV as the node’s centrality that corresponds to the significance of the agent within the socio-economic network. Using the polynomial algorithm developed by Aadithya, Ravindran, Michalak, & Jennings (2010) to compute SVs we analyze the way of creating new linkages to increase an agent’s significance (i.e., importance) in networks.

The Multifactor Model of the Agent's Power in Social Networks

The analysis of social reasoning is at the core of understanding how to manage social networks. Since interpersonal relations are composed of multiple factors with different nature (i.e., structural and social factors), we explore their influence on the strategizing processes in social networks. We formalize interpersonal relations using the methods of structural and social analysis. As a part of the research, we develop the soft-ware application for the numerical visualization of the social network functioning based on the proposed mechanism.

Critical objective function values in linear sum assignment problems

The linear sum assignment problem has been well studied in combinatorial optimization. Because of the integrality property, it is a linear programming problem with a variety of efficient algorithms to solve it. In the given research, we present a reformulation of the linear sum assignment problem and a Lagrangian relaxation algorithm for its reformulation. An important characteristic of the new Lagrangian relaxation method is that the optimal Lagrangian multiplier yields a critical bottleneck value. Lagrangian relaxation has only one Lagrangian multiplier, which can only take on a limited number of values, making the search for the optimal multiplier easy. The interpretation of the optimal Lagrangian parameter is that its value is equal to the price that must be paid for all objects in the problem to be assigned.

Centrality Computation in Weighted Networks Based on Edge-Splitting Procedure

The analysis of network’s centralities has a high-level significance for many real-world applications. The variety of game and graph theoretical approaches has a paramount purpose to formalize a relative importance of nodes in networks. In this paper we represent an algorithm for the centrality calculation in the domain of weighted networks. The given algorithm calculates network centralities for weighted graphs based on the proposed procedure of edges’ splitting. The approach is tested and illustrated based on different types of network topologies.