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We study a complex network model motivated by the network of citations among scholarly papers, in particular its dependence on the initial conditions. To reproduce the behaviour of rare papers that become highly cited only long after they are published, which are commonly referred to as sleeping beauties, we propose and study various model modifications. Whilst preserving the model's global behaviour, the sleeping beauty behaviour is indeed more pronounced in the modified models

In this thesis,we study a network model based on preferential attachment, aging of nodes and heterogeneous node fitness motivated by the network of scientific publications and citations among them. In the model, two phases can be distinguished. Before reaching an equilibrium, the initial phase of network growth is often dominated by a single node. We find the average final degree of such nodes and give estimations for the network size needed for this node to be âabsorbedâ by the degree distribution. The aging in the model induces a cut-off in the degree distribution different from the expected cut-off due to the limited size of a network. To determine the position of this cut-off we impose the limit of gaining at maximum one link per time-step in numerical calculations and compare the resulting final degree of nodes with the analytically predicted final degree. A property observed in citation data but not reproduced by the model is a correlation between the indegree of the citing papers and the in-degree of the cited paper. We modify the model and reproduce the observed degree-degree correlation in simulations using the modification we made.