Literacy: When Is a Network Model Explanatory?
Network analysis relies strongly on network models for several reasons: they show that a certain structure can be generated by a set of simple rules, they predict certain behaviors and functions, and they can be used as null-models. In this chapter, the q
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Literacy: When Is a Network Model Explanatory?
Abstract Network analysis relies strongly on network models for several reasons: they show that a certain structure can be generated by a set of simple rules, they predict certain behaviors and functions, and they can be used as null-models. In this chapter, the question discussed is whether the classic network models are likely to be explanatory network models for complex systems like metabolic networks, the internet, or collaboration networks.
12.1 Introduction As discussed in Chaps. 6 (Random Graphs and Network Models) and 7 (Random Graphs as Null Models), random graph models serve multiple purposes: • they can give a proof of concept that a complex, global structure can emerge from a simple, local rule; this is the primary purpose of the small-world model by Watts and Strogatz [43] and the scale-free network model by Barabási and Albert [4]. • they can generate a certain complex, global structure and have the additional advantage that the model’s expected structure is analyzable mathematically or at least empirically; for example, Kleinberg’s small-world model [23] is much easier to analyze mathematically than Watts and Strogatz’ model (s. Sect. 6.8). • they can explain how a given complex system creates some of the observed complex, global structure. This is what I call an explanatory network model (s. Sect. 6.6). It was the primary purpose of the model proposed by Vázquez, Flammini, and Vespignani, which is based on known, biochemical principles of gene duplication and which is able to reproduce important structural characteristics of the protein-protein interaction network [40] (s. p. 199). • they can be used as a null-model to find those patterns that are significantly different than expected in the random graph model.1
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common usage of terms, the term ‘random graph model’ will be used for random graph families used as a null-model, i.e., where it is expected that a real-world network deviates from randomness. The term ‘network model’ will be used for random graph families used as a model for the generation of a complex network in a complex system. © Springer-Verlag GmbH Austria 2016 K.A. Zweig, Network Analysis Literacy, Lecture Notes in Social Networks, DOI 10.1007/978-3-7091-0741-6_12
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12 Literacy: When Is a Network Modelexplanatory?
This enumeration defines a hierarchy of network models with a growing stringency with respect to their explanatory power: The first type of network model just needs to show that some mechanism is able to produce the observed result as a proof of concept; this is the least constraint. The most well-known classic network models belong to this class, like the small-world model or the preferential attachment model. However, and while their respective mechanism is not explanatory for most complex system of interest, it is neither totally arbitrary: all of their mechanisms are based on the intuition that nodes make their own decisions on their connections. Thus, the mechanisms follow a decentralized, local d
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