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Influence et contagion
L'influence et la contagion dans la cyberculture
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Multilayer Networks tutorial | #SNA #models

These are the slides for a tutorial talk about "multilayer networks" that I gave at NetSci 2014. I walk people through a review article that I wrote with my …
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Classifying Multilayer Networks


•  Special cases of multilayer networks include: mulplex networks, interdependent networks, networks of networks, node-­‐colored networks, edge-­‐colored mulgraphs, …


• To obtain one of these special cases, we impose constraints on the general structure defined earlier.




Other Types of  Multilayer Networks


•  k-­‐partite graphs

– Bipartite networks are most commonly studied


• Coupled-­‐cell networks

– Associate a dynamical system with each node of a multigraph. Network structure through coupling terms.


• Multilevel networks – Very popular in social statistics literature (upcoming special issue of Social Networks)

– Each level is a layer

– Think ‘hierarchical’ situations. Example: ‘micro-­‐ level’ social network of researchers and a ‘macro-­‐ level’ for a research-­‐exchange network between laboratories to which the researchers belong.

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Selection and Influence in Cultural Dynamics

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One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become similar to others they interact with) and selection (the tendency to be affected most by the behavior of others who are already similar). Influence tends to promote homogeneity within a society, while selection frequently causes fragmentation. When both forces are in effect simultaneously, it becomes an interesting question to analyze which societal outcomes should be expected. 

In order to study the joint effects of these forces more formally, we analyze a natural model built upon active lines of work in political opinion formation, cultural diversity, and language evolution. Our model posits an arbitrary graph structure describing which "types" of people can influence one another: this captures effects based on the fact that people are only influenced by sufficiently similar interaction partners. In a generalization of the model, we introduce another graph structure describing which types of people even so much as come in contact with each other. These restrictions on interaction patterns can significantly alter the dynamics of the process at the population level. 

For the basic version of the model, in which all individuals come in contact with all others, we achieve an essentially complete characterization of (stable) equilibrium outcomes and prove convergence from all starting states. For the other extreme case, in which individuals only come in contact with others who have the potential to influence them, the underlying process is significantly more complicated; nevertheless we present an analysis for certain graph structures.

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