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1

Modeling acquaintance networks based on balance theory

Vukašinović V., Šilc J., Škrekovski R.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 3

683--696

EN

An acquaintance network is a social structure made up of a set of actors and the ties between them. These ties change dynamically as a consequence of incessant interactions between the actors. In this paper we introduce a social network model called the Interaction-Based (IB) model that involves well-known sociological principles. The connections between the actors and the strength of the connections are influenced by the continuous positive and negative interactions between the actors and, vice versa, the future interactions are more likely to happen between the actors that are connected with stronger ties. The model is also inspired by the social behavior of animal species, particularly that of ants in their colony. A model evaluation showed that the IB model turned out to be sparse. The model has a small diameter and an average path length that grows in proportion to the logarithm of the number of vertices. The clustering coefficient is relatively high, and its value stabilizes in larger networks. The degree distributions are slightly right-skewed. In the mature phase of the IB model, i.e., when the number of edges does not change significantly, most of the network properties do not change significantly either. The IB model was found to be the best of all the compared models in simulating the e-mail URV (University Rovira i Virgili of Tarragona) network because the properties of the IB model more closely matched those of the e-mail URV network than the other models.

2

Czy sieci rządzą światem? : od Eulera do Barabasiego

Tarapata Z.

Biuletyn Instytutu Systemów Informatycznych

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2012

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nr 10

31-51

PL

W pracy poruszono problem różnorodnych zastosowań modeli i metod teorii grafów i sieci. W szczególności zwrócono uwagę na cechy charakterystyczne współczesnych sieci rzeczywistych. Przeanalizowano, w jaki sposób modeluje się te sieci, jakie mają własności i co z tego wynika. Poruszono algorytmiczne aspekty sieci złożonych ukierunkowane na złożoność obliczeniową metod wyznaczania wartości charakterystyk sieci. Kilkanaście interdyscyplinarnych przykładów rzeczywistych sieci zilustrowało opisywane własności sieci. We wnioskach opisano tendencje rozwojowe współczesnej teorii grafów i sieci, zwłaszcza w kontekście modelowania ewolucji sieci złożonych.

EN

In the paper problem of multi-applications of graph and networks theory models and methods is considered. The paper is especially focused on specific features of real networks. Analysis methods of these networks, their properties and what result from these analyses are discussed. Algorithmic aspects focused on computational complexity of methods to compute values of network's characteristics are considered. Several interdisciplinary examples of real networks illustrate network's properties being described. In conclusions current and future trends in development of complex networks are considered.

3

Simulation and Measurement of Complex Network Growth: the Interplay of Uniform and Preferential Attachment

Luo H., Horadam K.

Fundamenta Informaticae

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2008

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Vol. 84, nr 1

61-79

EN

The main discovery of the paper is the introduction and study of a new U-P complex network model, which aims to describe and analyze many common-featured real-world complex networks. This model employs a new functional form of the network growth rule: a linear combination of preferential and uniform attachment. In particular, the degree distribution of the model is first studied by using the computer simulation method, while the exact solution is also obtained analytically.