3 Diffusion

In the context of sustainability and climate adaptation, behavior change often depends not only on individual decisions but also on the social networks through which information and behaviors spread. This chapter examines how the structure of social networks influences the diffusion of adaptations—behaviors or practices that help people adjust to new risks or environmental conditions.

3.1 Primer on interventions

Recall that a sustainability intervention is an effort to promote some sustainable behavior or set of behaviors through education, training, or other means.
In order to simulate interventions, we must develop a sub-model for interventions, starting with classification.
- Our models of interventions will not be totally disconnected from models of the social systems themselves. Intervention models will specify the expected mode of transmission hypothesized to be most important for the design of the intervention.
- Intervention models should specify the outcome variable. For now, we will use the simplest version of outcomes included by default in socmod agent-based model output.

3.2 Comparing seeding strategies for interventions

3.2.1 Motivation

We begin with a concrete example: health behavior interventions in rural Honduran villages. In a study by Aral and Christakis, the researchers used detailed network data to test whether targeting well-connected individuals could increase the spread of health-promoting behaviors. The intervention succeeded not because it directly reached everyone, but because the network structure amplified its effects.

This example also serves as the foundation for an agent-based modeling assignment in which we will explain how computational experiments help us understand and predict the effect of different seeding and other intervention strategies.

We will close by contrasting seeding strategies that ignore social structure, as in Airoldi and Christakis (2024), with those that leverage social structure, like Turner et al. (2023).

3.2.2 Network models and structure

To understand why structure matters, we explore a series of increasingly complex network models. We begin with deterministic models:

Ring networks, where each node is connected to a fixed number of neighbors.
Complete networks, where every node is connected to every other node.

These help us isolate basic features like clustering and distance. We then turn to stochastic models:

Erdős–Rényi random networks, where links are created with fixed probability.
Watts–Strogatz small-world networks, which combine high local clustering with occasional long-range ties.

The small-world model captures key features of real-world social networks: short average path lengths and local clustering. Examples from the original Watts and Strogatz paper—such as the U.S. power grid and the C. elegans neural network—illustrate how widespread these features are.

An unintuitive feature of many social networks is the friendship paradox: on average, your friends have more friends than you do. This emerges because well-connected individuals are more likely to appear in others’ networks. It affects who sees new behaviors early, who is most influential, and how we interpret network data. We include a visualization to illustrate this dynamic and emphasize the importance of precise language.

3.2.3 From structure to simulation

Agent-based models help us represent complexity by formalizing how cognition and social structure interact. Each component is modeled separately. Cognition refers to the processes agents use to evaluate and adopt behaviors—drawing on existing knowledge, experience, and social feedback. Social structure refers to constraints on who interacts with whom, shaped by acquaintanceship, geography, institutions, and chance. We model social structure as a network: a graph where nodes represent individuals and edges represent relationships through which information or influence can flow.

We design our simulations to evaluate different intervention strategies based on cognitive factors we deem most important, with social structure that is “good enough” for representing a real-world system. by vary which agents start with a given behavior or belief, a process often called seeding. For example, in a diffusion model, we might seed a behavior with the most connected individuals, a randomly selected group, or individuals located in a particular community. These differences allow us to explore how network structure interacts with initial conditions to shape diffusion outcomes—helping us identify strategies that are more robust, equitable, or efficient.

3.3 The general diffusion model

Cognition: how agents evaluate new behaviors;
Social behavior: how agents learn from others and adopt behaviors;
Network structure: who interacts with whom.

These components are modular, allowing us to isolate the effects of structure while holding behavior constant.

MODEL SKETCH HERE OF GENERAL DIFFUSION MODEL

Behavior choice and learning
Group and social structure
Outcome measure: simulated success rate

This flexible framework will carry through the rest of the course. In the next section, we extend this model to explore how homophily, asymmetry, and structural inequality affect adaptation outcomes.

3.4 Network structure patterns that shape and constrain adaptation

3.4.2 Homophily: choice and induced

Homophily is the tendency for similar individuals to associate. We distinguish two forms:

Choice homophily, where individuals actively prefer similar partners;
Induced homophily, where external constraints (e.g., institutions, geography) create segregation even without conscious preference.

Two empirical illustrations:

An analysis of remote-work-eligible occupations shows clustering by education, income, and race.
A study of minority students in a mostly white MBA program finds that homophily can foster solidarity and resilience.

![Placeholder: Plot that I created based on that data. ]

These examples show that homophily can inhibit or support adaptation, depending on the context.

We also discuss experimental results from Centola (2010, 2011), which show that homophilous networks can outperform random ones in spreading health behaviors—especially when reinforcement and social learning are important.

3.4.3 Asymmetric homophily and diffusion

In some cases, homophily is asymmetric. One group (often the minority) is more exposed to the other than vice versa. In the “Minority Incubator, Majority Reservoir” model, this asymmetry allows minority-originating adaptations to diffuse outward more effectively.

This structural asymmetry isn’t necessarily intentional—it can emerge from how connections are formed. Yet it has real implications for diffusion, visibility, and adaptation speed.

3.4.4 Core-periphery structure

In a core-periphery network, a dense core of well-connected individuals is surrounded by a sparsely connected periphery. This structure supports fast diffusion through the core but may limit peripheral influence.

The South Pacific Island case provides an example: core-periphery organization enabled stable adaptation strategies under conditions of uncertainty and risk. These designs may emerge deliberately or organically.

3.4.5 When ties break: cumulative loss

To illustrate the consequences of broken connections, we turn to Henrich’s study of tool diversity in Oceania. When long-range maritime ties between islands broke down, isolated communities lost complex technologies.

This example highlights how network fragmentation can halt or reverse cumulative cultural evolution—a key dynamic in adaptation and innovation.

3.4.6 Modeling implications

Using the same agent-based model, we simulate diffusion on homophilous and core-periphery networks. Holding cognition and social behavior constant, we find:

Some structures accelerate diffusion;
Some amplify inequality in who adopts adaptations;
Some slow or block spread entirely.

These outcomes underscore the importance of network design in policy, development, and sustainability work.

3.4.7 Conclusion

Social networks don’t just transmit information—they shape who hears what, when, and from whom. Homophily and core-periphery structures are not marginal—they are central to how behaviors spread, how inequality persists, and how sustainability strategies succeed or fail.

In the next chapter and lecture, we extend this framework to include identity, polarization, and the role of group norms. These additional dynamics interact with the structures introduced here—and complicate efforts to promote coordination, learning, or fairness across diverse populations.