Resources & References

"ancestry forms a directed acyclic graphs", "the graphs of matrilineal descent and patrilineal descent are trees"
Youtube Video (CGPGrey, 2014): Your Family Tree Explained
Youtube Video (CGPGrey, 2015): Brief History of the Royal Family
Youtube Video (D!NG, 2018): Cousins Explained
Wikipedia: Family tree of Confucius in the main line of descent

Food Webs

National Geographic: Food Web Fun
PBS: Antarctic Marine Food Web
Reddit (QueenGoomy on r/Minecraft): Minecraft Food Web

Four Colour Theorem

Article (Conversation, 2013): Putting maths on the map with the four colour theorem
Game: Four Colour Theorem
Blank World Map: https://www.freeusandworldmaps.com/html/World_Projections/WorldPrint.html

Good Will Hunting

Numberphile - The problem in Good Will Hunting
Tree Problem: https://medium.com/cantors-paradise/the-math-problems-from-good-will-hunting-w-solutions-b081895bf379

Handshaking Lemma

House Floor Plan - examples can be found on Google Search, or from real estate websites

Domain: https://www.domain.com.au/
Realestate: https://www.realestate.com.au/buy
School Building Plan: https://www.standrewsibanda.org/budget
House Floor Plan (Remodel): http://everybodyisageniusblog.blogspot.com/2013/01/remodel.html

Internet (Hyperlinks)

Wiki Game
Wikipedia: Internet Backbone

Leaves

Metabolic Network

Mike Bostock

Fisheye Distortion
512 Paths to the White House (Tree Network)
Among the Oscar Contenders, A Host of Connections (Social Network)
Constellations of Directors and Their Stars (Social Network)
Mapping Every Path to the N.F.L. Playoffs (Tree Networks)

Muddy City Problem

Other Bridge Problems:

21 Bridges of Manhattan: https://medium.com/urban-explorations/a-bridge-too-far-8164847fbe1d
Bridges of Paris

Phone Networks

Phylogenetic Tree

Public Transport Networks

Rival Factions (PBS Infinite Series)

Seven Bridges of Königsberg

TED-ed Talk (2016): How the Königsberg bridge problem changed mathematics - Dan Van der Vieren

Slime Mould

Youtube Video (Harvard Magazine, 2010): Slime mold form a map of the Tokyo-area railway system
Article (Wired, 2010): Slime Mold Grows Network Just Like Tokyo Rail System
Classroom Experiment (Science in School, 2014): Intelligent slime? A hands-on project to investigate slime moulds
Article (Vox, 2018): Slime mold plasmodium: How this brainless superorganism thinks

Social Networks

Facebook, Twitter, Instagram
Email chains/contact networks
Spread of disinformation: Post-Truth
The Wisdom and/or Madness of Crowds
Matthew Kushin - Teaching social network concepts: Fun class activity

Sprouts (Game)

Submarine Communications Cables

Submarine Cable Map: https://www.submarinecablemap.com/

Three Utilities Problem

Youtube Video (3Blue1Brown, 2017): Rediscovering Euler's formula with a mug (not that Euler's formula)

Zoo Maps

Other Ideas

Roommates/Friendships - Mutual friends
Ant colonies
Citation network
Buyer/seller reputation (e.g. eBay)
Knight's Tour (Chessboard) - Hamiltonian path

Irrigation systems
Trade routes
GPS routes (incl. One way roads)
Mail delivery

Doctors/patients interaction
Garbage collection
Criminal networks
Television networks/broadcast stations
Body organ connections (anatomy)

URL to Resources

https://nrich.maths.org/1068 orientation activity - discussing Eulerian paths

Other Resources:

Activity Ideas/Resources

Could use Cuisenaire rods (or paper strips) as edges (where different lengths represent weights of the edges)

- For paths, can compare the lengths directly

Can also label edges (in large-scale networks) using Uno or playing cards

Can use ball-and-stick molecular kits to produce 3-D networks (nodes - balls, sticks - edges)

- - Number of bonds available = degree
  - Double/triple bonds = multiple edges
  - Note: Not useful for weighted edges

Breaking down the Konigsberg problem using different example graphs (4, 5, 6 vertices) - is it possible? how many edge? how many vertices are odd degree/even degree? https://www.youtube.com/watch?v=CMvi52OHzo4

Word problems:

- In a group of nine people, one person knows two of the others, two people know each other, four each know five others, and the remaining two each know six others. Show that there are three people who all know each other. (drawing --> interpreting)

Unused Literacy Activities/Exit Tasks

Ranking Activity:

Get students to rank different networks (or paths), e.g. complexity, weight total

Spot the Difference (between multiple network diagrams)

Running Dictation - one side of the room has the instructions (and someone to read it), the other side of the room is where the diagram has to be drawn

E.g. could have 10 vertices, and only information about degree, e.g. deg(A)=1, deg(B) = 5

Concept Mapping

What I knew already/what I know now/what I want to learn about

(3-2-1) 3 things I learned today, 2 things I found interesting, 1 thing I have questions about

General questions in a bowl (about networks) - answer as a class

See: Bonus Lessons

Tools

Recommended:

GeoGebra (Recommended: Geometry or Classic)
NCTM Graph Creator (requires Flash)
Graph Online - (Best online tool in terms of usability and simplicity; also provides algorithm tools)
MolView (for Ball & Stick molecule models)
GraphTea
Free Graph Theory Software
Draw.IO
Creately
D3 Graph Theory and Simple Graph Playground
yEd Graph Editor
Dijkstra Explorer
Prim's Algorithm Solver
Directed Graph Editor

Other Tools: