The Econometric Analysis of Network Data

Bryan Graham, Aureo de Paula, Bryan Graham, Aureo de Paula

• Publisher: Academic Press
• Year: 2020
• ISBN:
  9780128117729
• Topic: Business
• Subtopic: Business Mathematics
• Index: Business

The Econometric Analysis of Network Data serves as an entry point for advanced students, researchers, and data scientists seeking to perform effective analyses of networks, especially inference problems. It introduces the key results and ideas in an accessible, yet rigorous way. While a multi-contributor reference, the work is tightly focused and disciplined, providing latitude for varied specialties in one authorial voice.

• Answers both 'why' and 'how' questions in network analysis, bridging the gap between practice and theory allowing for the easier entry of novices into complex technical literature and computation
• Fully describes multiple worked examples from the literature and beyond, allowing empirical researchers and data scientists to quickly access the 'state of the art' versioned for their domain environment, saving them time and money
• Disciplined structure provides latitude for multiple sources of expertise while retaining an integrated and pedagogically focused authorial voice, ensuring smooth transition and easy progression for readers
• Fully supported by companion site code repository
• 40+ diagrams of 'networks in the wild' help visually summarize key points

Chapter 1

Introduction

Bryan S. Graham^a; Áureo de Paula^{b a}Department of Economics, University of California - Berkeley, Berkeley, CA, United States
^bUniversity College London, CeMMAP, IFS and CEPR, London, United Kingdom

Abstract

In this chapter we provide the foundational vocabulary for discussing, describing and summarizing network data. The chapter includes basic definitions, concepts such as centrality and a discussion of phenomena such as homophily and the social multiplier.

Keywords

Network; Adjacency Matrix; Connectivity; Centrality; Homophily

Chapter Outline

• Paths, distance and diameter
• Measuring homophily
• Measuring agent centrality
  • Degree centrality
  • Refinements of degree centrality
  • Katz–Bonacich centrality
  • Outdegree-based centrality measures
• References

In this chapter we provide the foundational vocabulary for discussing, describing and summarizing network data like that shown in Fig. 1.1. This figure depicts buyer–supplier relationships among publicly traded firms in the United States. Each dot (node or vertex) in the figure corresponds to a firm. If a firm, say, United Technologies Corporation, supplies inputs to another firm, say Boeing Corporation, then there exists a directed edge (also referred to as link or tie)

from United Technologies to Boeing. The supplying firm (left node) is called the tail of the edge, while the buying firm (right node) is its head. The set of all such supplier–buyer relationships forms the graph $G(\mathcal{V},\mathcal{E})$

, a directed network or digraph defined on $N=\left|\mathcal{V}\right|$

vertices or agents (here publicly traded firms). The set $\mathcal{V}=\{1,\dots ,N\}$

includes all agents (firms) in the network and $\mathcal{E}\subseteq \mathcal{V}\times \mathcal{V}$

the set of all directed links (supplier–buyer relationships) among them.¹,² The number of nodes N is sometimes referred to as the order of the digraph and $\left|\mathcal{E}\right|$

, its size.³

Figure 1.1 US buyer–supplier production network, 2015. Sources: Compustat – Capital IQ and authors' calculations.

If i directs an edges to j, and j likewise directs and edge back to i, we say the link is reciprocated. In some sett...