Exploring the dynamics of social networks

1. Exploring the dynamics of social networks Aleksandar Tomašević University of Novi Sad, Faculty of Philosophy, Department of Sociology atomasev@uns.ac.rs

2. Lecture overview • Early notions of “social networks” • Modern social network analysis • Network dynamics – longitudinal network data • Computational methods – network simulations

3. Early notions of social networks • Sociologist Georg Simmel (1858 - 1918) – intersection of social circles; triads and dyads • Anthropology – kinship networks in small rural societies • Harvard revolution, Harrison White (1930- ) - birth of modern social network analysis

4. Kinship networks

5. Early notions of social networks • Sociologist Georg Simmel (1858 - 1918) – intersection of social circles; triads and dyads • Anthropology – kinship networks in small rural societies • Harvard revolution, Harrison White (1930- ) - birth of modern social network analysis

6. Modern SNA - Basics • Social network analysis relies heavily on (algebraic) graph theory • Social network is a model of real-life social relations and social interactions. Network consists of actors (graph nodes or vertices) and social relations (graph edges or ties). • Sociology studies various types of networks and classifies them according to their size, function and complexity.

7. Modern SNA – Ego networks • Ego network (personal network) consists of a focal actor/node (“ego”) and nodes to whom ego is directly connected (“alters”). • Expanded ego networks also include the ties among alters • For example, single Facebook profile can be analyzed as one ego network. Profile owner is “ego” and her friends are “alters”.

8. Modern SNA – Ego network

9. Modern SNA – Complete (full) network • Complete networks have no focal nodes • They gives us a “bird’s eye” perspective on the totality of relations and connections between the nodes • Complete networks are more suitable for studying network structure – Beauty is not in the eye of the beholder

10. Modern SNA – Complete network

11. Modern SNA – Complex networks • Networks and graphs are complex if they exhibit non-trivial topological features; they cannot be described with simple models such as random graphs and lattices. • In practice, we’re dealing with complex networks when we have real-life networks with large number of actors, who can form different types of relations. • Network complexity is not a simple by-product of network size. The interdependence of actors within these networks is difficult to analyze, and requires advanced methodological tools. • Example of complex network: Marvel Universe Social Graph

12. Network Dynamics – Longitudinal data • Previously described networks = “snapshots” of social relations and social structure • Longitudinal data gives us the information about various network states over time. Most common way to obtain such data are panel surveys. • Network dynamics – study of changes in network structure over time; network evolution • Example: the evolution of friendship networks of college freshmen

13. Friendship network – Time 1

14. Friendship network – Time 2

15. Friendship network – Time 3

16. Friendship network – Time 4

17. Friendship network – Time 5

18. Modelling network dynamics – Agent-based models • In social sciences, the most common method to study properties of complex phenomena is called agent-based modelling (ABM) or bottom-up modelling • The essential idea of ABM is to simulate the interactions of social actors (or agents) and then to examine the totality of those effects on network level and compare them to real data • Every ABM must contain definitions of: social actors, rules of behavior and the topology of interactions (in our case: network)

19. Modelling network dynamics – Stochastic network models • While definitions of actors and networks do no present a difficult challenge, there are different ways to define and specify their simulated behavior. • In social sciences, many ABMs are based on game theory or similar “rational” choice approaches. • On the other side, stochastic modelling uses statistical inference to approximate behavioral patterns of social network actors and fit them to the real data.

20. Modelling network dynamics – Stochastic network models • Goal of stochastic network models is to investigate network evolution (dependent variable) as function of: • structural network effects • explanatory actor variables (gender, age, etc.) • explanatory dyadic variables (e.g. number of classes two students have in common) • In practice, we simulate the behavior of social actors in order to gain an answer to question: “Why do network members connect in a certain manner?”

21. Modelling network dynamics – Stochastic network models • Common network effects include: • actors tend to form ties with popular actors • actors tend to form directed ties in order to establish reciprocity • actors tend to form ties with actors with whom they are already indirectly connected (mutual friends effect) – closing of triads • structural equivalence: actors tend to connect to actors who are connected with similar others in the similar manner!

22. Conclusions • Dynamics of complex networks are most challenging area of study in social network analysis and network science in general • Computational methods (simulations) are required in order to explain the emergence of complex network structure and behavioral patterns • Computational models are mostly agent-based, but they can be based on different methodological approaches (game theory, artificial intelligence, statistical inference).

23. Recommended literature • General network science (including social networks) • Newman, Mark (2010). Networks: An Introduction. Oxford University Press. • László Barabási, Network science – free online book (work in progress), http://barabasilab.neu.edu/networksciencebook/ • Agent-based models (general) • Epstein, Joshua and and Robert Axtel (1996). Growing Artificial Societies: Social Science From The Bottom Up. Bradford Books • Stochastic modelling: plenty of resources at www.stats.ox.ac.uk/~snijders/siena/ • Including SIENA software ( Simulation Investigation for Empirical Network Analysis)

24. Thank you for your attention! For additional questions, comments: E-mail: atomasev@uns.ac.rs ResearchGate: https://www.researchgate.net/profile/Aleksandar_Tomasevic/ Twitter: http://twitter.com/atomasevic