Network Analysis

Computational Social Science · 01
What Is This?

A practical introduction to network analysis for social scientists. Part 1 covers the core concepts; Part 2 walks through a published paper step by step. Designed for a 15–20 minute presentation.

Audience

Graduate students across disciplines. No network analysis background assumed; basic familiarity with regression is helpful.


Part 1 · Slide 1

Why Study Relationships, Not Just Individuals?

Most methods treat observations as independent rows. But many social phenomena are relational — who asks whom for study help reveals hidden learning communities that GPA alone cannot explain. Network analysis shifts the question from "what are this person's attributes?" to "what is their position in a web of relationships?"

Traditional Data
Name Age GPA Alice223.8 Bob233.5 Carol213.9 Dave243.2 Eve223.6
Each row = one person, independent
Network Data
Alice Bob Carol Dave Eve
Relationships create structure
Think of it this way: A resume tells you about a person. A phone log tells you about their world.
Part 1 · Slide 2

The Language of Networks

A network has two building blocks: nodes (actors) and edges (relationships). Mathematically, a network is a graph G = (V, E) where V is the vertex set and E the edge set. Everything else builds on these two. Three key distinctions:

Undirected
A B C
Symmetric: Aij = Aji. E.g. co-authorship.
Directed
A B C
Asymmetric: Aij ≠ Aji. E.g. citations.
Weighted
A B C w = 5 w = 1 w = 3
Aij ∈ ℝ (continuous). E.g. trade volume.
Part 1 · Slide 3

Who Is "Important"? Three Answers

"Importance" depends on what you mean. Click each measure below — watch the node sizes change and read why.

Alice Bob Carol Dave Eve
Degree: node size = number of connections. Bob has the most (3).
Degree centrality — simply count edges: CD(i) = ki / (n−1). Intuition: who has the most direct contacts? Bob wins with 3. The most popular kid at the party. Theory: based on the adjacency matrix row sum, normalized by max possible ties.
Key insight: No single "right" measure — each captures a different structural role. Choose based on your research question.
Part 1 · Slide 4

Finding Groups: Community Detection

Real networks are cliquish — dense within groups, sparse between them. Community detection algorithms discover these groups automatically from connections alone, no labels needed.

Community A Community B bridge
Dense within groups, sparse between — the dashed line is the only bridge

Intuition: find groups where members are more connected to each other than to outsiders — like identifying lunch tables in a high school cafeteria. The algorithm doesn't need labels; it discovers structure purely from the pattern of connections. This is powerful because the groups it finds often reveal real social divisions that surveys miss.

Part 1 · Slide 5

From Description to Inference

Network methods fall into two layers. Descriptive methods tell you what the network looks like; inferential models test why it looks that way.

Descriptive: What Does the Network Look Like?

01
Centrality Measures
Who is important? Degree, betweenness, eigenvector — each captures a different structural role. Covered in Slide 3.
02
Community Detection
Where are the clusters? Algorithms like Louvain optimize modularity to find dense subgroups automatically. Fast, scalable, widely used. Covered in Slide 4.

Inferential: Why Does the Network Look This Way?

Q
QAP
Do two networks correlate? Permutation-based test. E.g. do students who study together also hang out socially? Shuffle one matrix thousands of times and check if the real correlation is unusually strong.
E
ERGM
What drives tie formation? E.g. do students seek help from same-major peers (homophily), or from high-GPA classmates (popularity)? Like logistic regression for networks. Today's focus.
L
Latent Space
Embed nodes in a latent space where proximity predicts ties. E.g. map a classroom's friendship network into 2D — students close in the space are likely friends, revealing cliques invisible in raw data.
Today we focus on ERGM — our paper (Köhler et al. 2024) uses it to ask: what drives advice-seeking ties in an organization? Part 2 walks through this step by step.
Part 1 · Slide 6

Should You Use Network Analysis?

If you can answer "yes" to all three, network analysis is likely the right tool:

01
Relational Data?
Your data has pairs (who↔whom). If each row is an independent person with no ties, standard methods may suffice.
02
Position Matters?
Structural position (connections, brokerage, community) shapes outcomes beyond individual attributes. Network analysis captures what regression cannot.
03
Dependence Is the Story?
Observations are not independent — your friend's behavior affects yours, one country's policy spills over to neighbors.
Part 1 · Slide 7

From Idea to Paper: A Network Analysis Workflow

01
Define
What are nodes and edges? E.g. "Nodes = students; edge = asked for help at least twice." The most important decision.
02
Construct
Build edge list or adjacency matrix from survey / archival data. Visualize early to spot errors.
03
Describe
Density, centrality, communities — the network's descriptive statistics.
04
Model
Test hypotheses with ERGM, QAP, or latent space models (see Slide 5).
05
Robustness
Vary thresholds and measures; remove key nodes to test stability.
Now let's see this workflow in action. Part 2 walks through a real published paper — from research question to findings.

Part 2

Paper Walkthrough: Expertise & Advice Networks

Köhler, Rausch, Biemann & Büchsenschuss (2024). "Expertise and specialization in organizations: a social network analysis." European Journal of Work and Organizational Psychology, 34(2), 282–297. Open Access

Core question: Are you sought for advice because you're truly skilled — or simply because you're well-known?

Part 2 · Slide 1

Research Question & Core Concepts

This paper asks: What drives the formation of advice-seeking ties in an organizational network? Two competing explanations:

A
Individual Attributes
Expertise and specialization — people seek out whoever is truly skilled. Example: you ask the best Excel person about Excel, the best writer about writing.
B
Structural Effects
Reciprocity — you helped me, so I ask you back. Homophily — I ask people similar to me (same department, same age). Example: you don't ask the best person, you ask the person you already know.

Expert (Expertise): sustained superior performance — both breadth and depth, developed through long-term accumulation. Like a senior underwriter who masters all insurance products. In the network, experts are central — many people ask them about many topics.

Specialist (Specialization): mid-to-high competence on tasks others don't do — from division of labor, not necessarily long-term accumulation. Like the only person who knows the legacy claims system. In the network, specialists are peripheral — only people with that specific problem come to them.

Part 2 · Slide 2

From Raw Data to a Network

01
Who Was Studied
Company: a global insurance firm, risk analysis division
Sample: N = 344 employees, 78% response rate
Demographics: average age 47, average tenure 11 years, roughly gender-balanced
02
What Was Measured
29 skills self-assessed on a rating scale:
— 18 core insurance skills
— 7 software skills
— 4 social skills
Self-identity scales:
— "I consider myself an expert"
— "I consider myself a specialist"
Network nomination:
— "Who do you ask for advice?" (up to 5 names × 3 skill areas)
03
Company Records
From the HR database:
— Age
— Gender
— Tenure (years)
— Job level
— Leadership responsibility (yes/no)
Part 2 · Slide 3

Method: Three Studies in One Paper

The paper uses three studies that build on each other: first discover a pattern, then explain what drives it, then validate whether theoretical categories hold up.

Study 1: Spearman CorrelationsStudy 2: ERGMStudy 3: Optimal Matching
Question Is being asked for advice tied to your real skill, or just to being popular? What actually drives advice ties — after removing the network's own patterns? Do real skill profiles match theoretical expert/specialist templates?
Method Compute in-degree in 3 skill areas; correlate with self-rated skills (Spearman); compare correlations (Fisher z-test). Build models in 3 steps: (1) baseline (edges + reciprocity); (2) network effects (in-degree, brokerage); (3) personal traits (expertise, skills, tenure). Compare via AIC. R ergm. Sort each person's 29 skills high→low; compute "distance" to ideal profiles (R TraMineR); correlate with self-ratings and centrality.
Plain English Count who asks you in each area, then see if that number matches your actual ability — or just your popularity elsewhere. A logistic regression for networks — test which factors make two people more likely to form a "who asks whom" tie. Draw a template for "perfect expert" and "perfect specialist," then measure how far each person is from those templates.
Part 2 · Slide 4

Finding 1: The Halo Effect

Result: Cross-domain in-degree correlations are significantly stronger than within-domain skill–in-degree correlations (Fisher z, p < .05). Exception: core insurance skills, where actual competence also matters.

i.e.: Once colleagues see you as a go-to person for insurance, they also come to you for software and social problems — even if you're not actually good at those. Being asked reflects reputation, not skill-by-skill competence.

Part 2 · Slide 5

Finding 2: What Drives Advice Ties (ERGM)

+
Significant Positive
Reciprocity — strongest effect; you ask me, I ask you back.
Core & software skill level — higher skill averages attract more ties.
Expertise identity — small positive effect.
Tenure — longer-tenured get asked more.
=
Homophily
Software skill similarity — strongest; you ask peers at your level.
Similar tenure — joined around the same time → ask each other.
Same leadership level — managers ask managers.
Not Significant
Specialization — "only person who does X" ≠ more sought-after.
Social skills — no effect.
Brokerage — negative; people skip middlemen.

i.e.: The network rewards "you helped me before" (reciprocity) and "you're genuinely skilled" (skill level). People ask those who are similar to themselves. But being a "specialist" or having social skills doesn't attract advice ties.

Part 2 · Slide 6

Finding 3: Skill Profiles vs. Theory

E
Expert — Confirmed
Result: Higher self-rated expertise → closer to ideal expert profile. Higher in-degree → also closer. Theory and data align.
S
Specialist — Contradicted
Result: Higher self-rated specialization → farther from ideal specialist profile (opposite of expected). Two sub-types in the sample but the template only fits one.

i.e.: People who call themselves "experts" really do have broad, high skill sets — the label matches reality. But "specialist" means different things: some are the only lawyer in the office (broad within their niche), others handle one narrow task among peers. The theoretical template only captured the second type, so the match failed.

Part 2 · Slide 7

Contributions & Limitations

+
Contribution
Four-type framework (expert / non-expert / specialist / non-specialist) within each domain. Discovered halo effect in advice seeking. ERGM + optimal matching — rigorous network methods beyond simple correlations.
Limitations
Self-assessed skills (no objective test). 5-name cap may miss ties. Ego-network inferred as complete network. Cross-sectional — no causal direction. Specialist template only fits one sub-type.
?
Future Directions
Use objective KPIs instead of self-ratings. Interview to explore halo effect mechanisms. Differentiate two specialist sub-types. Replicate across organizations.

References

01
Today's Paper
Köhler, Rausch, Biemann & Büchsenschuss (2024). Expertise and specialization in organizations. EJWOP, 34(2), 282–297. Open Access
02
ERGM Tutorial
Statnet team. ERGM tutorial with R code and worked examples. statnet.org
03
Textbook
Wasserman & Faust (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.
ERGM Derivation
Step-by-step mathematical derivation of the ERGM formula — from network probability to logistic regression form. Read the derivation