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This chapter introduces the basic notions of graph theory and discusses the starting point of network science, namely the Konigsberg bridge problem. A few examples of different graphs, lattices, and fractals are considered. These are used to explain the notions of a node degree, the shortest path length, clustering and so on. Milgram's experiment is also considered, and the notion of a random network is explained. A fundamental difference between small worlds and lattices and fractals, is discussed.
Keywords: graph theory; random networks; degree; degree distribution; clustering; trees
Chapter. 4291 words. Illustrated.
Subjects: Mathematical and Statistical Physics
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