Graph Theory Problems: Shortest Paths, Strongly Connected Components, Isomorphism

Q1.
Given the weighted graph below, answer the following questions:
(1) Find the shortest path between node A and node H.
(2) Find the diameter of the graph and give a shortest path with a length equal
to the diameter.

Q2.
Given the directed graph below, answer the following questions:
(1 ) List all strongly connected components.
(2) Add an edge to make this graph strongly connected.

Q3.1.
Are these two graphs isomorphic? If yes, find a mapping between the nodes.

Q3.2.
Are these two graphs isomorphic? If yes, find a mapping between the nodes.

Q3.2.
Are these two graphs isomorphic? If yes, find a mapping between the nodes.

Q4.
Given the graph below, answer the following questions:
(1) Find all nodes with the lowest clustering coefficient.
(2) Find all nodes with the highest clustering coefficient.

Q5.
In the social network depicted below, with each edge labelled as either a strong
or weak tie, which nodes violate the Strong Triadic Closure property? Provide
an explanation for your answer.

Q6.
List all the maximal cliques present in the graph provided.

Q7.
Given the graph below, answer the following questions:
(1) Show the BFS process starting from node A.
(2) Compute the betweenness of paths starting from node A.

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