1. Node Count ($n$): Identify the number of individual points.
2. Edge Count ($e$): Identify the number of connections.
3. Completeness: A graph is "Complete" ($K_n$) if $e = n(n-1)/2$.
4. Knot Check: A knot is an unbroken loop that crosses over/under itself.
For each community description, give the number of Nodes and Edges.
The Trinity: 3 persons, each connected to the other two.
The Hub Church: A leader and 10 members. Each member is ONLY connected to the leader.
The Mesh Cell: 4 friends where everyone is connected to everyone else.
How many edges are needed to make a Complete Network for the following groups?
A family of 5 people.
The 12 Apostles.
A small city of 100 people.
In the "Hub Church" problem (Part I), if the leader leaves, how many separate pieces does the graph break into? In the "Mesh Cell" problem, if one person leaves, is the rest of the group still connected? Explain why Redundant Edges are the key to a healthy community.
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Look at the two drawings below.
Circle the one that is a True Knot (cannot be untied without cutting).
You have two separate networks, each with 5 nodes.
Task: What is the MINIMUM number of edges you need to add to make the whole group of 10 nodes one single connected manifold?
What happens if that one bridge is cut?
Objective: Explain Networks to a younger student using a ball of yarn.
The Activity:
1. Stand in a circle with friends.
2. Toss the yarn to someone while holding the end.
3. Keep tossing until everyone is holding part of the web.
4. "Try to step out of the circle without pulling anyone else."
The Lesson: "In the Kingdom, we are all 'Knotted' together by the yarn of God's love. when one person moves, we all feel the pull!"
Response: ___________________________________________________________