Articulation Points & Bridges

Question 1

What is an articulation point ?

Answer 1

An articulation point is a vertex that when removed (along with it’s edges) creates more components in the graph.

After removing a vertex , graph becomes articulation point.

Question 2

Back Edge

Answer 2

a Back Edge is an edge that connects a vertex to a vertex that is discovered before it’s parent

If the node has any child whose subtree doe snot have a backedge, then it is a articulation point.

Question 3

What are articulation points in a network?

Answer 3

Articulation points, also known as cut vertices, are nodes in a network whose removal would increase the number of connected components within the network.

Question 4

What is the significance of articulation points in network theory?

Answer 4

Articulation points represent critical nodes; their deletion would lead to the fragmentation of the network into disconnected components, impacting network connectivity and robustness.

Question 5

Define bridges in a network.

Answer 5

Bridges, also called cut edges, are edges in a network whose removal would increase the number of connected components in the network if eliminated.

Question 6

Why are bridges important in network analysis?

Answer 6

Bridges are crucial as they identify edges whose elimination would cause the network to split into disjoint segments, influencing network structure and connectivity.

Question 7

How do articulation points and bridges contribute to network resilience?

Answer 7

Identifying these critical elements helps in understanding the vulnerability of a network to node or link failures, enabling network administrators to enhance network robustness and fault tolerance.

Question 8

What is an articulation point in graph theory?

Answer 8

An articulation point, also known as a cut vertex, is a vertex in an undirected graph such that its removal increases the number of connected components in the graph.

Question 9

How does the removal of an articulation point impact a graph?

Answer 9

Removing an articulation point disconnects the graph or splits it into two or more separate subgraphs, highlighting the importance of that vertex in maintaining the graph’s connectivity.

Question 10

How are articulation points identified in graphs?

Answer 10

Algorithms like Tarjan’s algorithm or depth-first search (DFS) are used to identify articulation points within a graph by analyzing the graph’s structure and connectivity.

Question 11

Can you provide an example of an articulation point in a social network graph?

Answer 11

In a social network graph, an articulation point might represent a person whose removal divides the network into multiple disconnected communities, impacting the overall cohesion of the network.

Question 12

What distinguishes an articulation point from a bridge in a graph?

Answer 12

An articulation point is a vertex whose removal increases the number of connected components, while a bridge is an edge whose removal has the same effect by disconnecting the graph.

Question 13

Back Edge

Answer 13

A back edge in a graph traversal, like depth-first search (DFS), is an edge that connects a vertex to one of its ancestors in the DFS tree. It forms a cycle in the graph and indicates that there is a path from a vertex back to one of its ancestors in the traversal.

Question 14

Back Edge in DFS:

Answer 14

Definition: In a DFS traversal of an undirected or directed graph, a back edge is an edge that connects a vertex to an ancestor vertex in the DFS tree formed during the traversal.

Characteristics: A back edge indicates the presence of a cycle in the graph. It connects a vertex back to one of its ancestors in the DFS tree, forming a loop or cycle within the graph.

Detection: During DFS traversal, encountering a visited vertex (other than the parent) that has an edge to one of its ancestors represents a back edge.

Use in Graph Analysis: Identifying back edges is crucial in algorithms that deal with cycle detection in graphs, such as checking for cycles in a graph, finding strongly connected components in directed graphs, or topological sorting.

Question 15

Back Edge

Answer 15

A back edge is an edge that connects a vertex to an ancestor in a graph traversal (like DFS) that is not its direct parent in the traversal tree.
In an undirected graph, a back edge can form a cycle by connecting a vertex back to one of its ancestors.
In a directed graph, a back edge connects a vertex to an ancestor, possibly indicating a cycle or a loop in the graph.

Question 16

Low/Discovery Time:

Answer 16

Low and discovery times are associated with vertices during depth-first search (DFS) traversal in a graph.
Discovery time (or ‘discovery’ or ‘entry time’) of a vertex is the time when a vertex is first discovered or visited during the DFS traversal.
Low time (or ‘low’ or ‘exit time’) of a vertex is the earliest discovery time of any vertex reachable from the subtree rooted at that vertex, including the vertex itself.

Question 17

Discovery Time

Answer 17

Records when a vertex is first encountered in the traversal.

Question 18

Low Time:

Answer 18

Represents the earliest vertex reachable from the subtree rooted at the current vertex (including itself).The low value of a vertex helps in determining the root of a strongly connected component.