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# Sum of degrees of all nodes of a undirected graph

Given an edge list of a graph we have to find the sum of degree of all nodes of a undirected graph.
Example

Examples:

`Input : edge list : (1, 2), (2, 3), (1, 4), (2, 4)  Output : sum= 8`

Brute force approach
We will add the degree of each node of the graph and print the sum.

## C++

 `// C++ implementation of above approach``#include ``using` `namespace` `std;` `// returns the sum of degree of all``// the nodes in a undirected graph``int` `count(``int` `edges[][2], ``int` `len, ``int` `n)``{``    ``int` `degree[n + 1] = { 0 };` `    ``// compute the degree of each node``    ``for` `(``int` `i = 0; i < len; i++) {` `        ``// increase the degree of the``        ``// nodes``        ``degree[edges[i][0]]++;``        ``degree[edges[i][1]]++;``    ``}` `    ``// calculate the sum of degree``    ``int` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``sum += degree[i];` `    ``return` `sum;``}` `// main function``int` `main()``{``    ``// the edge list``    ``int` `edges[][2] = { { 1, 2 },``                       ``{ 2, 3 },``                       ``{ 1, 4 },``                       ``{ 2, 4 } };``    ``int` `len = ``sizeof``(edges) / (``sizeof``(``int``) * 2), n = 4;` `    ``// display the result``    ``cout << ``"sum = "` `<< count(edges, len, n) << endl;``    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG {` `    ``// returns the sum of degree of all``    ``// the nodes in a undirected graph``    ``static` `int` `count(``int` `edges[][], ``int` `len, ``int` `n)``    ``{``        ``int` `degree[] = ``new` `int``[n + ``1``];` `        ``// compute the degree of each node``        ``for` `(``int` `i = ``0``; i < len; i++) {` `            ``// increase the degree of the``            ``// nodes``            ``degree[edges[i][``0``]]++;``            ``degree[edges[i][``1``]]++;``        ``}` `        ``// calculate the sum of degree``        ``int` `sum = ``0``;``        ``for` `(``int` `i = ``1``; i <= n; i++)``            ``sum += degree[i];` `        ``return` `sum;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``// the edge list``        ``int` `edges[][] = { { ``1``, ``2` `},``                          ``{ ``2``, ``3` `},``                          ``{ ``1``, ``4` `},``                          ``{ ``2``, ``4` `} };``        ``int` `len = edges.length, n = ``4``;` `        ``// display the result``        ``System.out.println(``"sum = "` `+ count(edges, len, n));``    ``}``}` `// This code has been contributed by 29AjayKumar`

## Python3

 `# Python 3 implementation of above approach` `# returns the sum of degree of all``# the nodes in a undirected graph``def` `count(edges, len1, n):``    ``degree ``=` `[``0` `for` `i ``in` `range``(n ``+` `1``)]` `    ``# compute the degree of each node``    ``for` `i ``in` `range``(len1):``        ``# increase the degree of the``        ``# nodes``        ``degree[edges[i][``0``]] ``+``=` `1``        ``degree[edges[i][``1``]] ``+``=` `1` `    ``# calculate the sum of degree``    ``sum` `=` `0``    ``for` `i ``in` `range``(``1``, n ``+` `1``, ``1``):``        ``sum` `+``=` `degree[i]` `    ``return` `sum` `# main function``if` `__name__ ``=``=` `'__main__'``:``    ``# the edge list``    ``edges ``=` `[[``1``, ``2``], [``2``, ``3``], [``1``, ``4``], [``2``, ``4``]]``    ``len1 ``=` `len``(edges)``    ``n ``=` `4` `    ``# display the result``    ``print``(``"sum ="``, count(edges, len1, n))``    ` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG {` `    ``// returns the sum of degree of all``    ``// the nodes in a undirected graph``    ``static` `int` `count(``int``[][] edges, ``int` `len, ``int` `n)``    ``{``        ``int``[] degree = ``new` `int``[n + 1];` `        ``// compute the degree of each node``        ``for` `(``int` `i = 0; i < len; i++) {` `            ``// increase the degree of the``            ``// nodes``            ``degree[edges[i][0]]++;``            ``degree[edges[i][1]]++;``        ``}` `        ``// calculate the sum of degree``        ``int` `sum = 0;``        ``for` `(``int` `i = 1; i <= n; i++)``            ``sum += degree[i];` `        ``return` `sum;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``// the edge list``        ``int``[][] edges = ``new` `int``[][] { ``new` `int``[] { 1, 2 },``                                      ``new` `int``[] { 2, 3 },``                                      ``new` `int``[] { 1, 4 },``                                      ``new` `int``[] { 2, 4 } };``        ``int` `len = edges.Length, n = 4;` `        ``// display the result``        ``Console.WriteLine(``"sum = "` `+ count(edges, len, n));``    ``}``}` `// This code has been contributed by Code_Mech.`

## Javascript

 ``

## PHP

 ``

Output

```sum = 8

```

Space complexity: O(n) as it uses an array of size n+1 (degree array) to store the degree of each node.

Time complexity: O(n) as it iterates through the edges array.
Efficient approach
If we get the number of the edges in a directed graph then we can find the sum of degree of the graph. Let us consider an graph with no edges. If we add a edge we are increasing the degree of two nodes of graph by 1, so after adding each edge the sum of degree of nodes increases by 2, hence the sum of degree is 2*e.

## C++

 `// C++ implementation of above approach``#include ``using` `namespace` `std;` `// returns the sum of degree of all``// the nodes in a undirected graph``int` `count(``int` `edges[][2], ``int` `len)``{``    ``return` `2 * len;``}` `// main function``int` `main()``{``    ``// the edge list``    ``int` `edges[][2] = { { 1, 2 },``                       ``{ 2, 3 },``                       ``{ 1, 4 },``                       ``{ 2, 4 } };``    ``int` `len = ``sizeof``(edges) / (``sizeof``(``int``) * 2);` `    ``// display the result``    ``cout << ``"sum = "` `<< count(edges, len) << endl;``    ``return` `0;``}`

## Java

 `// Java implementation for above approach``class` `GFG {` `    ``// returns the sum of degree of all``    ``// the nodes in a undirected graph``    ``static` `int` `count(``int` `edges[][], ``int` `len)``    ``{``        ``return` `2` `* len;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``// the edge list``        ``int` `edges[][] = { { ``1``, ``2` `},``                          ``{ ``2``, ``3` `},``                          ``{ ``1``, ``4` `},``                          ``{ ``2``, ``4` `} };``        ``int` `len = edges.length;` `        ``// display the result``        ``System.out.println(``"sum = "` `+ count(edges, len));``    ``}``}` `// This code contributed by Rajput-Ji`

## Python 3

 `# Python3 implementation of above approach` `# returns the sum of degree of all``# the nodes in a undirected graph``def` `count(edges, length) :``    ` `    ``return` `2` `*` `length;` `# Driver Code``if` `__name__ ``=``=` `"__main__"` `:` `    ``# the edge list``    ``edges ``=` `[[ ``1``, ``2` `],``             ``[ ``2``, ``3` `],``             ``[ ``1``, ``4` `],``             ``[ ``2``, ``4` `]];``    ``length ``=` `len``(edges);` `    ``# display the result``    ``print``(``"sum = "``, count(edges, length));` `# This code is contributed by Ryuga`

## C#

 `// C# implementation for above approach``using` `System;` `class` `GFG {` `    ``// returns the sum of degree of all``    ``// the nodes in a undirected graph``    ``static` `int` `count(``int``[, ] edges, ``int` `len)``    ``{``        ``return` `2 * len;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``// the edge list``        ``int``[, ] edges = { { 1, 2 },``                          ``{ 2, 3 },``                          ``{ 1, 4 },``                          ``{ 2, 4 } };``        ``int` `len = edges.GetLength(0);` `        ``// display the result``        ``Console.WriteLine(``"sum = "` `+ count(edges, len));``    ``}``}` `/* This code contributed by PrinciRaj1992 */`

## Javascript

 `   `

## PHP

 ``

Output

```sum = 8

```

Space complexity: O(1)

Time complexity: O(1)

Another approach(Naive Approach):

We can iterate through the edge list and count the degree of each node. This can be done by creating a dictionary that maps each node to its degree, and then summing up the degrees of all nodes.

1. Create a variable sum and initialize it to 0.This variable will store the sum of degrees of all nodes in the graph and iterate over all nodes in the graph.
2. The FOR loop iterates over all nodes in the graph, where N is the total number of nodes in the graph. For each node i, it counts the number of edges that are incident on i (i.e., that have i as one of their endpoints), by iterating over all edges in the edge list and checking if i is one of their endpoints. The degree of node i is equal to the number of such edges. The degree of node i is then added to the sum and return the sum of degrees of all nodes:
3. Returns the sum calculated in the previous stepand in the main function, create an edge list and call the countDegrees function to find the sum of degrees of all nodes:

Here is the implementation of above approach

## C++

 `#include ``#include ``using` `namespace` `std;` `int` `countDegrees(``int` `edges[][2], ``int` `len)``{``    ``// create a dictionary to store degrees of nodes``    ``unordered_map<``int``, ``int``> degrees;` `    ``// iterate over all edges and count the degree of each``    ``// node``    ``for` `(``int` `i = 0; i < len; i++) {``        ``degrees[edges[i][0]]++;``        ``degrees[edges[i][1]]++;``    ``}` `    ``// sum up the degrees of all nodes``    ``int` `sum = 0;``    ``for` `(``auto` `d : degrees) {``        ``sum += d.second;``    ``}` `    ``return` `sum;``}` `// main function``int` `main()``{``    ``// the edge list``    ``int` `edges[][2]``        ``= { { 1, 2 }, { 2, 3 }, { 1, 4 }, { 2, 4 } };``    ``int` `len = ``sizeof``(edges) / (``sizeof``(``int``) * 2);` `    ``// display the result``    ``cout << ``"sum = "` `<< countDegrees(edges, len) << endl;``    ``return` `0;``}`

## Java

 `import` `java.util.HashMap;``import` `java.util.Map;` `public` `class` `GFG {` `    ``// Function to count the degrees of nodes in an edge list``    ``public` `static` `int` `countDegrees(``int``[][] edges) {``        ``// Create a HashMap to store degrees of nodes``        ``Map degrees = ``new` `HashMap<>();` `        ``// Iterate over all edges and count the degree of each node``        ``for` `(``int``[] edge : edges) {``            ``degrees.put(edge[``0``], degrees.getOrDefault(edge[``0``], ``0``) + ``1``);``            ``degrees.put(edge[``1``], degrees.getOrDefault(edge[``1``], ``0``) + ``1``);``        ``}` `        ``// Sum up the degrees of all nodes``        ``int` `sum = ``0``;``        ``for` `(``int` `degree : degrees.values()) {``            ``sum += degree;``        ``}` `        ``return` `sum;``    ``}` `    ``// Main function``    ``public` `static` `void` `main(String[] args) {``        ``// The edge list``        ``int``[][] edges = { { ``1``, ``2` `}, { ``2``, ``3` `}, { ``1``, ``4` `}, { ``2``, ``4` `} };` `        ``// Display the result``        ``System.out.println(``"sum = "` `+ countDegrees(edges));``    ``}``}`

## Python3

 `from` `collections ``import` `defaultdict` `def` `count_degrees(edges):``    ``degrees ``=` `defaultdict(``int``)` `    ``# iterate over all edges and count the degree of each node``    ``for` `edge ``in` `edges:``        ``degrees[edge[``0``]] ``+``=` `1``        ``degrees[edge[``1``]] ``+``=` `1` `    ``# sum up the degrees of all nodes``    ``total_degrees ``=` `sum``(degrees.values())` `    ``return` `total_degrees` `# main function``def` `main():``    ``# the edge list``    ``edges ``=` `[[``1``, ``2``], [``2``, ``3``], [``1``, ``4``], [``2``, ``4``]]` `    ``# display the result``    ``print``(``"sum ="``, count_degrees(edges))` `if` `__name__ ``=``=` `'__main__'``:``    ``main()`

## C#

 `using` `System;``using` `System.Collections.Generic;` `namespace` `DegreeCounting``{``    ``class` `Program``    ``{``        ``static` `int` `CountDegrees(``int``[,] edges)``        ``{``            ``// Create a dictionary to store degrees of nodes``            ``Dictionary<``int``, ``int``> degrees = ``new` `Dictionary<``int``, ``int``>();` `            ``// Iterate over all edges and count the degree of each node``            ``for` `(``int` `i = 0; i < edges.GetLength(0); i++)``            ``{``                ``int` `node1 = edges[i, 0];``                ``int` `node2 = edges[i, 1];` `                ``if` `(!degrees.ContainsKey(node1))``                    ``degrees[node1] = 0;``                ``if` `(!degrees.ContainsKey(node2))``                    ``degrees[node2] = 0;` `                ``degrees[node1]++;``                ``degrees[node2]++;``            ``}` `            ``// Sum up the degrees of all nodes``            ``int` `sum = 0;``            ``foreach` `(``var` `degree ``in` `degrees.Values)``            ``{``                ``sum += degree;``            ``}` `            ``return` `sum;``        ``}` `        ``static` `void` `Main(``string``[] args)``        ``{``            ``// The edge list``            ``int``[,] edges = {``                ``{ 1, 2 }, { 2, 3 }, { 1, 4 }, { 2, 4 }``            ``};` `            ``// Display the result``            ``Console.WriteLine(``"sum = "` `+ CountDegrees(edges));``        ``}``    ``}``}`

Output

```sum = 8

```

Time complexity: O(len), where len is the length of the edge list
Auxiliary Space: O(N), where N is the total number of nodes in the graph