Overview
This week shifts focus from individual nodes and local structures to understanding networks at a higher level of abstraction, a critical skill for analyzing complex organizational and market systems. We explore two complementary approaches to seeing social structure, drawing on foundational sociological theory:
Connectionist approaches: Focusing on social cohesion and the formation of communities through direct ties and resource flows. This view aligns with Durkheim’s concept of solidarity, asking what holds groups together. In a business context, this helps identify siloed departments, informal communication clusters, and the robustness of information flow.
Positional approaches: Focusing on roles and positions that emerge through similar patterns of ties (structural equivalence). This abstracts away from who knows whom to what function an actor serves (e.g., “broker,” “leader,” “isolate”). This is essential for organizational design, identifying redundant roles, and understanding power dynamics beyond simple hierarchy.
These perspectives help us address fundamental questions about social integration and structure: How do we identify meaningful subgroups? How do role structures organize economic and social life? And how can these insights drive strategic decision-making?
Prepare
📖 Review:
📖 Required Readings:
Chapter 8: “Cohesion and Groups” (Rawlings et al., 2023)
Focus on:
Ridge Structures: How networks are composed of peaks of high connectivity and ridges of lower connectivity.
Modularity: The measure of the strength of division of a network into modules (communities).
Small Worlds: The balance between local clustering and global reachability, and its implication for diffusion (e.g., of innovation or risk).
Chapter 10: “Positions and Roles” (Rawlings et al., 2023)
Focus on:
Structural Equivalence: Actors who have identical ties to and from all other actors.
Regular Equivalence: Actors who have ties to equivalent others (e.g., two managers may not know the same people, but they both supervise employees and report to directors).
Blockmodeling: The inductive method for identifying these roles from data.
Practice
Advanced tutorial on Blockmodeling and Structural Equivalence:
Identifying Roles: Using CONCOR and hierarchical clustering to find actors with similar behavioral profiles.
Image Matrices: Creating simplified maps of how roles interact (e.g., “How does Sales interact with Engineering?”).
Model Fit: Evaluating how well your reduced model represents the complex reality.
Application: Analyzing a corporate advice network to identify key influencers and bottlenecks.
Ponder
Discussion Questions
1. Mechanical vs. Organic Solidarity in Modern Firms Durkheim distinguished between mechanical solidarity (based on similarity) and organic solidarity (based on interdependence). How do communities (clusters of dense ties) and role structures (interdependent positions) map onto these concepts? Which form of solidarity is more prevalent in a startup vs. a large bureaucracy?
2. The “Small World” of Business Watts and Strogatz (1998) showed that a few random links can drastically reduce the diameter of a network. In a business context, what are the risks and benefits of a “small world” network? Consider the spread of innovation vs. the spread of systemic risk (e.g., financial contagion).
3. Methodological Pluralism Why is there no single “best” algorithm for community detection? What does this imply about the nature of social groups? As an analyst, how do you justify your choice of method to a stakeholder who wants “the right answer”?
Core Readings
Cohesion: Borgatti, S. P., et al. (2024). Analyzing Social Networks Using R. Chapter 8.
Blockmodeling: White, H. C., Boorman, S. A., & Breiger, R. L. (1976). Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology.
Supplementary Readings
Small Worlds: Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature.
Weak Ties: Granovetter, M. S. (1973). The strength of weak ties. American Journal of Sociology.
Robust Action: Padgett, J. F., & Ansell, C. K. (1993). Robust action and the rise of the Medici. American Journal of Sociology. (A classic example of using network position for political power).
Additional Resources
R packages:
igraph: Community detection, blockmodelingsna and network: Role equivalence, structural cohesionblockmodeling: Generalized blockmodeling
Python packages:
igraph: Community detection algorithmsnetworkx: Modularity, community detectionpython-louvain: Louvain algorithm implementationleidenalg: Leiden algorithm
Visualization:
- Gephi: Interactive community visualization
- Cytoscape: Network analysis and visualization
- R packages:
ggraph, visNetwork