In this thesis results of research from several different areas of complex networks theory have been introduced. First, generalized versions of network descriptors such as transmission, betweeness centrality, networkness and network surplus have been defined and analyzed. Two different approaches that were studied both take into account the assumption that vertices in networks, which are closer to each other, communicate more than the vertices on greater distances. In the first case the amount of communication between vertices has been amended by \(d(u, v)^\lambda\)where \(\lambda < 0\) and in the second case by \(\lambda^{d(u,v)}\), where \(d(u, v)\) represents the distance between vertices \(u\) and \(v\), and \(\lambda \in (0, 1)\). Upper and lower bounds for minimal and maximal values of these descriptors have been analyzed. Furthermore, special kind of networks has been defined. Curriculum network is a simple, directed graph in which vertices represent educational units, and directed arc from \(u\) to \(v\) indicates that understanding of a unit \(u\) is necessary for learning and understanding of unit \(v\). Measures for evaluating the quality of curriculum content sequencing have been proposed and analyzed from sever different points of view. Graphs corresponding to most and least complex curricula have been found. Some real-world curriculum networks and their properties have been analyzed. Finally, the problem of community detection in curriculum networks has been analyzed and two algorithms for solving this problem have been suggested.