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This chapter reviews diffusion of innovations theory which has been the theory that has used network principles and perspectives most extensively. An introduction to the theory and a review of its principles is provided. The chapter then reviewed the 4 major classes of diffusion models (1) integration/opinion leadership, (2) structural models, (3) critical levels, and (4) dynamic models. All four models explicitly account for network diffusion dynamics, but vary in their mathematical rigor and complexity. The chapter also introduced the calculation of infectiousness and susceptibility which dynamically account for adoption behavior and in-degree and out-degree, respectively. Empirical data illustrating network exposure effects are presented as well as the calculation and interpretation of network thresholds. The chapter closes with a brief critique of the theory.

This chapter describes statistical methods for inferring and quantifying social transmission in groups of animals in the wild, or in “captive” groups of animals in naturalistic social environments. In particular, it considers techniques for analyzing time-structured data on the occurrence of a particular behavior pattern, or behavioral trait, in one or more groups. For the most part, the focus is on cases where a novel trait spreads through one or more groups. Following standard terminology in the field of social learning, the spread of a trait through a group is referred to as a diffusion, and the resulting data as diffusion data. The methods include diffusion curve analysis and network-based diffusion analysis. For the latter, inclusion of individual-level variables is taken into account, along with model selection and inference, modeling of multiple diffusions, choosing a social network, and “untransmitted” social effects. The chapter also examines the spatial spread of a behavioral trait.

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.