Connecting Elements

Discrete Math · Axiom Academy

INTRO Social Network Connections Explore how relationships work in a social network and discover patterns that emerge from different types of connections! Click on two people to create a connection between them. Try making some mutual friendships and some one-way follows ! Explore which types of relationships have a special symmetry property . Click on different relationship types to see examples! If Alex is friends with Blake, and Blake is friends with Casey, does that mean Alex is friends with Casey? Explore this transitivity question! Real social networks combine all these relationship types. Explore this network and discover interesting patterns! You explored relations – connections between elements in a set. Relations can have special properties like symmetry (goes both ways) and transitivity (chains together). These aren't just social network concepts – they're fundamental to discrete mathematics! In mathematics, we study relations with specific properties: reflexive (relates to itself), symmetric (goes both ways), transitive (chains work), and antisymmetric (one-way only). Different combinations create different types of mathematical structures! Understanding relations helps us model databases, analyze social networks, design recommendation systems, optimize delivery routes, and solve countless computational problems. The properties you discovered are the building blocks of graph theory and computer science!

This is the written version of the interactive lesson above. See the full Discrete Math course.