Introducing Middle School Students to Graph Theory Please

Introducing Middle School Students to Graph Theory

Please connect the three triangles to the circle using nonintersecting lines.

Now try this one

Challenge: Is this even possible? One gets stuck….

You have been creating graphs represented by what are called nodes and edges. Nodes: are the point or shape that was being connected sometimes called vertices Edges: are the lines that connect the nodes sometimes referred to as arcs. The entire picture/graph is called a network. Edg e This is a special type of graph Node

What do we observe about nodes and edges? graph? Some of the nodes are different sizes What possible reason can you give for this observations? The number of connections a node has changes the size of the node Edg e What do you observe about the Node

Network Generators Recreate an already known network based on a set of instructions. Sometimes these generators group them into communities based on the relationships between nodes. Sometimes the communities are overlapping or in the style of a Venn Diagram. We will be learning what these different graphs look like and recreating our own networks to show a relationship within science topics.

Relationship Nodes that are connected have a relationship. One node that has many nodes connected to it creates a community. How many communities do you see in the graph to the right?

Venn Diagrams in Graph Theory

Can you label the nodes, edges, and communities?

Nodes: Dots Edges: Lines