For each part, give a brief one-sentence answer. (a) Consider a particular forest, and make a graph where each vertex is a different animal species that lives in that forest.
There is an edge from A to B if A is known to eat B.
For example, if there are owls and mice in this forest then there would be an edge from the owl vertex to the mouse vertex.
i. Explain why this graph is a directed graph.
ii. What is the definition of the indegree of a vertex and what is its meaning in this graph?
ii. What is the definition of the outdegree of a vertex and what is its meaning in this graph?
iv. What is the definition of a source and what would it mean if this graph has a source?
v. What is the definition of a sink and what would it mean if this graph has a sink?
vi. What does it mean if this graph has a cycle?
vii. What does it mean if there is a path from A to B?
(b) Consider a graph where each vertex is a student at UCSD, and there is an edge from A to B if A and B are taking the same class this quarter.
i. Explain why this is an undirected graph.
ii. How would you interpret the meaning of the degree of a vertex in this graph?
iii. Estimate the degree of the vertex that represents you.
iv. Briefly describe a situation in which this graph would have more than one connected component.