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Complexity and Emergence in Economic and Social Systems

Networks and Emergence in Complex Systems

Explore how large-scale patterns emerge from the structure of interactions among individual components.

17.5h (5 days)

€1,199

Face-to-face

English

Program date: July 6-10, 2026

Early bird deadline: April 15, 2026

Learn more

Complexity and Emergence in Economic and Social Systems

Networks and Emergence in Complex Systems

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Who is this Course for?

Complexity and Emergence in Economic and Social Systems

Networks and Emergence in Complex Systems

Course overview

This course explores how large-scale patterns emerge from the structure of interactions among individual components. We study networks as the backbone of complex systems in economics, sociology, and the natural sciences. The focus is on phase transitions, scaling laws, and collective phenomena, moving beyond descriptive network measures toward an understanding of how connectivity gives rise to macro-level regularities.

The learning objectives of the course include:

Understand fundamental concepts of graph theory and how they model real-world interaction structures.
Analyze emergent properties such as percolation, phase transitions, and the formation of giant components.
Connect network topology to economic and social outcomes (contagion, coordination, diffusion).
Recognize and interpret scaling regularities in networked systems (e.g., degree distributions, firm-size and city-size laws).
Acquire hands-on experience with network data and simulations.

Faculty

Who is this course for?

This course has been designed for:

Graduate students, early-career researchers, and advanced undergraduates in economics, sociology, political science, and applied mathematics.

Learning outcomes

By the end of the course, students will be able to:

Derive basic analytical results for random graphs and percolation thresholds
Simulate contagion and diffusion processes on networks
Identify scaling behavior in empirical and simulated data
Relate network features to stability, resilience, and efficiency in social and economic systems

Key topics for Networks and Emergence in Complex Systems course

This course will cover the following topics:

Day 1 - Networks as Representations of Complex Systems

Morning (Theory)

Networks as a modeling language for interactions
Types of networks: social, economic, technological, biological
Graph representation and basic topology: adjacency matrix, degree, components
Empirical examples from economics (production networks, interbank networks, R&D networks)

Afternoon (Practicals)

Construct and visualize networks in Python (NetworkX) or R (igraph)
Compute and interpret basic topological features

Day 2 - Random Graphs and Phase Transitions

Morning (Theory)

Erdős–Rényi model G(n,p): connectivity and emergence of the giant component
Analytical derivation of the critical threshold
Phase transitions and criticality in networks
Scaling near critical points

Afternoon (Practicals)

Simulate Erdős–Rényi graphs for varying p
Plot size of the largest component vs. p
Identify phase transition empirically

Day 3 - Preferential Attachment, Scaling, and Heterogeneity

Morning (Theory)

Preferential attachment and the Barabási–Albert model
Derivation of power-law degree distributions
Universality of scaling exponents in social and economic systems
Empirical scaling laws: firm sizes, cities, and wealth distributions

Afternoon (Practicals)

Simulate preferential attachment.
Estimate scaling exponents in simulated and real data
Discuss Zipf’s law and Gibrat’s law in economics

Day 4 - Contagion, Diffusion, and Information Cascades

Morning (Theory)

Diffusion models: simple contagion, threshold models, and SIR epidemics
Cascade conditions and network resilience
Coordination games and peer effects on networks
Economic contagion (financial crises, technology adoption)

Afternoon (Practicals)

Simulate diffusion and cascade models
Compare spread dynamics across random, small-world, and scale-free topologies

Day 5 - Criticality, Synchronization, and Collective Phenomena

Morning (Theory)

Self-organized criticality and sandpile models on networks
Percolation and resilience under node removal
Synchronization and collective oscillations (Kuramoto model)
Connection to macroeconomic volatility and systemic risk

Afternoon (Practicals)

Implement sandpile and percolation simulations
Explore synchronization dynamics
Discussion of project ideas and empirical applications

List of References

Here is a list of texts that may help you to prepare for this course.

Networks as Representations of Complex Systems

Newman, M. E. J. (2010). Networks: An Introduction, Ch. 1–2.
Jackson, M. O. (2008). Social and Economic Networks, Ch. 1–2.
Barabási, A.-L. (2016). Network Science, Ch. 1.

Random Graphs and Phase Transitions

Newman (2010), Ch. 12.
Bollobás, B. (2001). Random Graphs, Ch. 1–3.
Bianconi, G. (2018). Multilayer Networks: Structure and Function, Ch. 2.

Preferential Attachment, Scaling, and Heterogeneity

Barabási (2016), Ch. 5–7.
Gabaix, X. (1999). “Zipf’s Law for Cities.” Quarterly Journal of Economics, 114(3):739–767.
Newman (2005). “Power Laws, Pareto Distributions and Zipf’s Law.” Contemporary Physics, 46(5):323–351

Contagion, Diffusion, and Information Cascades

Easley, D., & Kleinberg, J. (2010). Networks, Crowds, and Markets, Ch. 19–21.
Jackson, M. O. (2023). Networks in the Social and Information Sciences, Ch. 7–8.
Pastor-Satorras, R., & Vespignani, A. (2001). “Epidemic Spreading in Scale-Free Networks.” Physical Review Letters, 86(14).

Criticality, Synchronization, and Collective Phenomena

Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality.
Barabási (2016), Ch. 8.
Strogatz, S. H. (2001). Exploring Complex Networks. Nature, 410:268–276

Why join our Summer School?

All BSE Summer courses are taught to the same high standard as our Master’s programs. Join us to:

1

Network with like-minded peers

2

Study in vibrant Barcelona

3

Learn from world-renowned faculty

Mix and match your summer courses!

Remember that you can combine this program with courses in any of the other BSE Summer School programs (schedule permitting). Maximise your learning this summer and take advantage of our multiple-course discount.

Admissions and Requirements

All BSE Summer School applicants must meet the entrance requirements.

Program date: July 6-10, 2026

Early bird deadline: April 15, 2026

Requirements

Summer School applicants normally demonstrate one or more of the following:

A strong background in Economics or a field closely related to the course topic (Statistics, Law, etc.)
Postgraduate degree or current Master’s/PhD studies related to the course topic
Relevant professional experience

Requirements for Networks and Emergence in Complex Systems course

A solid foundation in linear algebra and probability theory, with some prior exposure to dynamical systems or microeconomic modeling.

Schedule

Here is your schedule for this edition of BSE Networks and Emergence in Complex Systems course.

Time

6

mon

7

tue

8

wed

9

thu

10

fri

11:30-13:30

Lecture

16:15-17:45

Practical

Credit Transfers (ECTS)

To be eligible for credit transfer, students must complete a final project.

Students will deliver a short final project one week after the summer school finishes. It will consist in solving a final problem that will include the practical and empirical issues worked on in class.

Consult the Summer School Admissions page for more information about this option.

Certificate of Attendance

Participants who attend more than 80% of the course will receive a Certificate of Attendance, free of charge.

Fees

Multiple course discounts are available; see more information about available discounts. Fees for other courses listed in other Summer School programs may vary.

Course

Networks and Emergence in Complex Systems

Agent-Based Modeling for Economics and the Social Sciences

Modality

Face-to-face

Total Hours

17.5

ECTS

1

Regular Fee

1,199€

Reduced Fee*

699€

* Reduced Fee applies for PhD or Master’s students, Alumni of BSE Master’s programs, and participants who are unemployed.

FAQ

Here are some commonly asked questions by participants. Any further queries, please contact our Admissions Team.

Can I see the full Summer School calendar?

You can view the full Summer School calendar here.

Is accommodation included in the course fee?

Accommodation is not included in the course fee. Participants are responsible for finding accommodation.

Are the sessions recorded?

Sessions will NOT be recorded; however, the materials provided by the professor will be available for a month after the course has finished.

How much does each Summer School course cost?

Fees for each course may vary. Please consult each course page for accurate information.

Are there any discounts available?

Yes, BSE offers a variety of discounts on its Summer School courses. See more information about available discounts or request a personalized discount quote by email.