Hypernetworks in Scalable Open Education Jeffrey Johnson Cristian Jimenez-Romero Alistair Willis European TOPDRIM (DYM-CS), Etoile, & GSDP Projects & Complexity and Design Research Group www.complexitanddesign.org The Open University, UK ECCS 2013 Barcelona
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Hypernetworks in Scalable Open Education Jeffrey Johnson Cristian Jimenez-Romero Alistair Willis European TOPDRIM (DYM-CS), Etoile, & GSDP Projects & Complexity.
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Hypernetworks in Scalable Open Education
Jeffrey JohnsonCristian Jimenez-Romero
Alistair Willis
European TOPDRIM (DYM-CS), Etoile, & GSDP Projects&
Complexity and Design Research Groupwww.complexitanddesign.org
The Open University, UK
ECCS 2013 Barcelona
16th September 2013
Networks can represent relationships between pairs, < x, y >
e.g. student x studies with student y
Hypernetworks
Networks can represent relationships between pairs, < x, y >
e.g. student x studies with student y
What about relationships between three students, < x, y, z >
e.g. x, y and z all study together.
Hypernetworks
Networks can represent relationships between pairs, < x, y >
e.g. student x studies with student y
What about relationships between three students, < x, y, z >
e.g. x, y and z all study together. Or a relation between 4 ?
Hypernetworks
Networks can represent relationships between pairs, < x, y >
Or relations between any number of things …
Hypernetworks
The generalisation of an edge in a network is a simplex
Simplices can represent n-ary relation between n vertices
The generalisation of an edge in a network is a simplex
A p-dimensional simplex has p+1 vertices
A 1-simplex a, b has 2 vertices A 2-simplex a, b, c has 3 vertices
A 3-simplex a, b, c, d has 4 vertices A p-simplex v0, v1, … vp has p+1 vertices