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|All Authors / Contributors:||
Nataša Kejžar; Vladimir Batagelj
|Description:||VIII, 147 str. : graf. prikazi ; 30 cm.|
Network analysis is a multidisciplinary field in which units along with the relationships among them are studied. We concentrate on the development and analyses of different time-evolving network models. Real-world networks are evolving and growing over time, hence it is relevant to try to understand their evolutionary rules and principles. While real-world complete networks are often impossible to collect, models representing their best approximations are studied instead. We define a new framework of probabilistic inductive classes of graphs (PICGs). The new definition is an extension of inductive classes of graphs by imposing the probability space in the choice of initial graphs, rules and their left elements. Many known network models can be cast as PICGs. We present some probabilistic results regarding the size and order of some PICG models and (approximately) determine the network degree distribution. Another stochastic network model definition is also given.The so-called feedback network model (which evolves by creating vertices and cycles that enable a feedback process) is motivated by the social sciences. It does not fit within the PICGs framework. With simulations, we observe the evolution of relevant statistical network properties: the average shortest path, the ratio between the number of vertices and links and degree distribution. Lastly, a different perspective on the evolving vertex degree distribution is given. We propose an approach to clustering temporal citation distributions in order to obtain relevant and informative temporal citation patterns. These patterns are useful in the field of scientometrics where the temporal importance of works is evaluated with citation indices.