Introduction to Graph Theory: Nodes and Edges

A graph has 5 nodes labeled A, B, C, D, and E. It has edges AB, AC, BD, DE, and CE. How many nodes and how many edges are in the graph?

In a graph, what is the difference between a node and an edge? Give a real-world example of each.

A friendship graph shows four students: Maya, Luis, Priya, and Jordan. Maya is friends with Luis and Priya. Luis is friends with Jordan. Priya is friends with Jordan. List all the edges in the graph.

Look at a graph with nodes P, Q, R, and S. The edges are PQ, QR, RS, and SP. Draw the graph and describe its shape.

A graph has nodes A, B, C, and D. Every pair of nodes is connected by exactly one edge. How many edges does the graph have?

The degree of a node is the number of edges that touch it. In a graph, node X is connected to A, B, C, and D. What is the degree of node X?

A road map can be modeled as a graph. Suppose towns are nodes and roads are edges. If there is a road from Town A to Town B and a road from Town B to Town C, but no road from Town A to Town C, what edges should be included?

A graph has 7 nodes and 0 edges. What does this tell you about the connections in the graph?

In the graph with edges AB, AC, BC, CD, and DE, find the degree of node C.

Create a simple graph to model a group project with 5 students. Each edge should mean that two students worked together. Your graph must have at least 4 edges. Then write the list of edges you used.