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Introduction
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This introductory chapter sets the scene for the material which follows by briefly introducing the study of networks and describing their wide scope of application. It discusses the role of well-specified random graphs in setting network science onto a firm scientific footing, emphasizing the importance of well-defined null models. Non-trivial aspects of graph generation are introduced. An important distinction is made between approaches that begin with a desired probability distribution on the final graph ensembles and approaches where the graph generation process is the main object of interest and the challenge is to analyze the expected topological properties of the generated networks. At the core of the graph generation process is the need to establish a mathematical connection between the stochastic graph generation process and the stationary probability distribution to which these processes evolve.
Title: Introduction
Description:
This introductory chapter sets the scene for the material which follows by briefly introducing the study of networks and describing their wide scope of application.
It discusses the role of well-specified random graphs in setting network science onto a firm scientific footing, emphasizing the importance of well-defined null models.
Non-trivial aspects of graph generation are introduced.
An important distinction is made between approaches that begin with a desired probability distribution on the final graph ensembles and approaches where the graph generation process is the main object of interest and the challenge is to analyze the expected topological properties of the generated networks.
At the core of the graph generation process is the need to establish a mathematical connection between the stochastic graph generation process and the stationary probability distribution to which these processes evolve.
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