Network-Oriented Modeling has successfully been applied to obtain network models for a wide range of phenomena, including Biological Networks, Mental Networks, and Social Networks. In this chapter, it is discussed how the interpretation of a network as a causal network and taking into account dynamics in the form of temporal-causal networks, brings more depth. Thus main characteristics for a network structure are obtained: Connectivity in terms of the connections and their weights, Aggregation

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... f multiple incoming connections in terms of combination functions, and Timing in terms of speed factors. The basics and the scope of applicability of such a Network-Oriented Modelling approach are discussed and illustrated. This covers, for example, Social Network models for social contagion or information diffusion, and Mental Network models for cognitive and affective processes. From the more fundamental side, it will be discussed how emerging network behavior can be related to network structure. Keywords Network-Oriented Modeling Á Temporal-causal network Introduction Network-Oriented Modeling is a relatively new way of modeling that is especially useful to model intensively interconnected and interactive processes. It has been applied to model networks for biological, mental, and social processes, and still more. The aim of this chapter is to discuss the ins and outs of this modeling perspective in more detail, without considering network reification yet, as that will be the subject of Chap. 3. It is discussed how the interpretation of a network as a causal network and taking into account dynamics brings more depth in the Network-Oriented Modeling perspective, leading to the notion of temporal-causal network as introduced in (Treur 2016). In a temporal-causal network, nodes represent states with values that vary over time, and connections represent causal relations describing how states affect each other. The wide scope of applicability (Treur 2016, 2017) of such a Network-Oriented Modelling approach will be discussed and illustrated. This covers, for example, network models for principles of social contagion or information diffusion, and network models for mental processes. When network reification as introduced in more detail in Chap. 3 is also taken into account, many kinds of adaptive network models are covered, for example for principles of evolving social networks, such as the homophily principle, or for Hebbian learning in Mental Networks. From the methodological side, it will be discussed how mathematical analysis can be used to identify the relation between emerging behaviour of the network and network structure. In this chapter, in Sect. 2.2 first the conceptual background of Network-Oriented Modeling is discussed, leading to a conceptual representation of a temporal-causal network, which defines such a network. Next, in Sect. 2.3 the numerical foundation is discussed, including a precise definition of a numerical representation by which a temporal-causal network model gets its intended dynamic semantics, and which can be used for simulation and analysis. Section 2.4 introduces role matrices as a useful specification format for temporal-causal networks. In Sect. 2.5 the interesting challenge to determine how emerging network behaviour relates to network structure and some results on this relation are briefly discussed. In Sect. 2.6 the scope of applicability is discussed. Finally, Sect. 2.7 is a discussion. Network-Oriented Modeling: Conceptual Background Network-Oriented Modeling is applied in a wide variety of areas. The general pattern is that some type of process in some domain X is described by a network structure, and this type of network is called an X Network or X Network model. Note that such a network is considered as a modelling concept, not as reality. Some examples are: • Modeling the dynamics of propagation of chemical activity in cells based on the concentration levels of chemicals by Biological Network models • Modeling the dynamics of propagation of neural activity based on activation levels of neurons by Neural Network models • Modeling the dynamics of propagation of mental activity based on engaging mental states by Mental Network models • Modeling the dynamics of propagation of individual activity based on activation of personal states by Social Network models; e.g., -Information diffusion; e.g., in social media -Opinion spread; e.g., in political campaigns -Emotion contagion; e.g., one smile triggering the other -Activity contagion; e.g., following each other These are just four types of domains X where processes, in reality, are modelled by network models, which then can be called X Networks with X = Biological, Neural, Mental, or Social. 26 2 Ins and Outs of Network-Oriented Modeling