## WHAT IS THE edge connectivity?

The minimum number of edges whose deletion from a graph disconnects. , also called the line connectivity. The edge connectivity of a disconnected graph is 0, while that of a connected graph with a graph bridge is 1.

## How is edge connectivity calculated?

The minimum number of edges whose removal makes ‘G’ disconnected is called edge connectivity of G. In other words, the number of edges in a smallest cut set of G is called the edge connectivity of G. If ‘G’ has a cut edge, then λ(G) is 1. (edge connectivity of G.)

**What is edge connectivity of KN?**

The maximum value of k for which G remains k-edge-connected is called its edge connectivity, κ (G). What is κ (Kn)? It is n − 1 again, because every vertex has degree n − 1 and to disconnect a vertex we have to remove these edges.

### What is edge connectivity of K 3 4?

2 votes. in K3,4 graph 2 sets of vertices have 3 and 4 vertices respectively and as a complete bipartite graph every vertices of one set will be connected to every vertices of other set.So total no of edges =3*4=12.

### How do I find maximum edge-connectivity?

Simple Graph

- The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2.
- The number of simple graphs possible with ‘n’ vertices = 2nc2 = 2n(n-1)/2.

**What does 2 edge connected mean?**

A connected graph is 2–edge connected if it remains connected whenever any edges are removed. A bridge (or cut arc) is an edge of a graph whose deletion increases its number of connected components, i.e., an edge whose removal disconnects the graph.

## Which graph is more connected?

A directed graph is strongly connected if there is a path between any two pair of vertices. For example, following is a strongly connected graph. It is easy for undirected graph, we can just do a BFS and DFS starting from any vertex. If BFS or DFS visits all vertices, then the given undirected graph is connected.

## Is edge connected graph?

In graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph is the largest k for which the graph is k-edge-connected.

**How do you calculate connectivity?**

The connectivity index is calculated by dividing the number of nodes by the number of links by the number of nodes.

### Is a 3 connected graph also 2-connected?

A graph being 2-connected just means that you need to remove at least 2 vertices to disconnect it. This means that a 3-connected graph is also 2-connected and a 2-connected graph could possibly be 3-connected. An example of a 2-connected but not 3-connected graph would be any cycle graph with at least 4 vertices.

### What is the vertex connectivity and edge connectivity?

In words: vertex-connectivity is at most edge-connectivity, which is always at most the smallest degree. Let v be a vertex with degree δ(G). The edge cut for the set {v} has δ(G) edges, so an edge cut with δ(G) edges exist, and the minimum edge cut has size at most δ(G).

**What is the edge connectivity of a graph?**

The edge connectivity λ of the graph G is the minimum number of edges that need to be deleted, such that the graph G gets disconnected.

## What is the edge-connectivity of G1?

The edge-connectivity λ ( G) of a connected graph G is the smallest number of edges whose removal disconnects G. When λ ( G) ≥ k, the graph G is said to be k -edge-connected. G1 has edge-connectivity 1.

## What is Stoer-Wagner algorithm for edge connectivity?

Special algorithm for edge connectivity. The task of finding the edge connectivity if equal to the task of finding the global minimum cut. Special algorithms have been developed for this task. One of them is the Stoer-Wagner algorithm, which works in $O(V^3)$ or $O(V E)$ time.

**What is the vertex connectivity of a graph?**

It is clear, that the vertex connectivity of a graph is equal to the minimal size of such a set separating two vertices s and t, taken among all possible pairs ( s, t). The Whitney inequalities (1932) gives a relation between the edge connectivity λ, the vertex connectivity κ and the smallest degree of the vertices δ: