## What is the rank of a incidence matrix of a connected graph?

The rank of complete incidence matrix is (n-1), where n is the number of nodes of the graph. The order of incidence matrix is (n × b), where b is the number of branches of graph.

## How do you find the incidence matrix on a graph?

The incidence matrix of a graph G is a |V| ×|E| matrix. The element aij= the number of times that vertex viis incident with the edge ej.

**What is an incidence matrix in graph theory?**

The incidence matrix of a directed graph is a matrix B where n and m are the number of vertices and edges respectively, such that if the edge leaves vertex , 1 if it enters vertex. and 0 otherwise (many authors use the opposite sign convention).

### How do you find the connectedness of a graph?

A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair of vertices. An undirected graph that is not connected is called disconnected.

### What is incidence matrix in network topology?

An Incidence Matrix represents the graph of a given electric circuit or network. Hence, it is possible to draw the graph of that same electric circuit or network from the incidence matrix. We know that graph consists of a set of nodes and those are connected by some branches.

**Which of the following is true for incidence matrix for graph theory?**

We can draw a graph with the help of the incidence matrix. The algebraic sum of elements of all the columns is zero. The rank of the incidence matrix is (n–1). The determinant of the incidence matrix of a closed loop is zero.

## What is planar graph in discrete mathematics?

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.

## What is incidence matrix and its properties?

Properties of Complete Incidence Matrix : Each row in the matrix corresponds to a node of the graph. Each row has non zero entries such as +1 and -1 depending upon the orientation of branch at the nodes. Also the entries in all other columns of that row are zero.

**What is incidence matrix and adjacency matrix?**

Note: An incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. An adjacency matrix is a square matrix utilized to describe a finite graph.

### What do you mean by connected components of a graph?

Connected Component Definition A connected component or simply component of an undirected graph is a subgraph in which each pair of nodes is connected with each other via a path.