14  Introduction

When we look at a network, we don’t just want to describe what we see. We want to understand why the connections exist and how they shape the bigger picture. That’s where statistical network models come in. Unlike purely descriptive approaches, models enable us to infer the underlying processes that generate network structures.

What makes modeling a powerful statistical tool is that they don’t just summarize the data we already have, but instead dig deeper to uncover the hidden rules that shape the network. They let us test ideas, explore patterns, and even predict how networks might evolve. Of course, no model can fully capture the complexity of the real world, but they provide useful blueprints for understanding the mechanisms forming and driving the system.

14.1 The Challenges of Network Modeling

Most traditional data analysis treats the world like a collection of independent units; people, companies, events, each with their own neatly packaged characteristics. This monadic approach assumes that what happens to one entity has no impact on another, much like strangers sitting silently in a waiting room. This assumption, known as independent and identically distributed (i.i.d.) data, underlies most statistical models.

But network data laughs in the face of independence. Here, the unit of observation isn’t the individual, but the relationships between them; whether it’s friendships, collaboration or trade agreements. These relationships (or ties) don’t exist in isolation; they overlap, influence each other, and evolve in complex ways. When walking down the street, you do not let the flip of a coin determine whether you will befriend a by-passer or not.

A defining feature of network data is that one tie can change the likelihood of another forming. Think of social circles: if Alice and Bob are both friends with Carol, odds are Alice and Bob will become friends too. This phenomenon (triadic closure), explains everything from friend groups to why your LinkedIn keeps suggesting you connect with your ex’s new colleague.

Unlike spatial or temporal dependencies, where values near each other in space or time are correlated, network dependencies aren’t just noise to correct for; they’re the main event. Instead of being a nuisance, these dependencies are precisely what we study to understand how networks form and evolve.