---
id: 5900f3d91000cf542c50feea
title: 'Problem 107: Minimal network'
challengeType: 1
forumTopicId: 301731
dashedName: problem-107-minimal-network
---

# --description--

The following undirected network consists of seven vertices and twelve edges with a total weight of 243.

<img class="img-responsive center-block" alt="Network with seven vertices and twelve edges" src="https://cdn.freecodecamp.org/curriculum/project-euler/minimal-network-1.png" style="background-color: white; padding: 10px;">

The same network can be represented by the matrix below.

|   | A  | B  | C  | D  | E  | F  | G  |
|---|----|----|----|----|----|----|----|
| A | -  | 16 | 12 | 21 | -  | -  | -  |
| B | 16 | -  | -  | 17 | 20 | -  | -  |
| C | 12 | -  | -  | 28 | -  | 31 | -  |
| D | 21 | 17 | 28 | -  | 18 | 19 | 23 |
| E | -  | 20 | -  | 18 | -  | -  | 11 |
| F | -  | -  | 31 | 19 | -  | -  | 27 |
| G | -  | -  | -  | 23 | 11 | 27 | -  |


However, it is possible to optimise the network by removing some edges and still ensure that all points on the network remain connected. The network which achieves the maximum saving is shown below. It has a weight of 93, representing a saving of 243 − 93 = 150 from the original network.

<img class="img-responsive center-block" alt="Network with seven vertices and left six edges: AB, BD, CA, DE, DF, EG" src="https://cdn.freecodecamp.org/curriculum/project-euler/minimal-network-2.png" style="background-color: white; padding: 10px;">

Using `network`, an 2D array representing network in matrix form, find the maximum saving which can be achieved by removing redundant edges whilst ensuring that the network remains connected. Vertices not having connection will be represented with `-1`.

# --hints--

`minimalNetwork(testNetwork)` should return `259679`.

```js
assert.strictEqual(minimalNetwork(_testNetwork), 259679);
```

# --seed--

## --after-user-code--

```js
const _testNetwork = [
  [-1,-1,-1,427,668,495,377,678,-1,177,-1,-1,870,-1,869,624,300,609,131,-1,251,-1,-1,-1,856,221,514,-1,591,762,182,56,-1,884,412,273,636,-1,-1,774],[-1,-1,262,-1,-1,508,472,799,-1,956,578,363,940,143,-1,162,122,910,-1,729,802,941,922,573,531,539,667,607,-1,920,-1,-1,315,649,937,-1,185,102,636,289],[-1,262,-1,-1,926,-1,958,158,647,47,621,264,81,-1,402,813,649,386,252,391,264,637,349,-1,-1,-1,108,-1,727,225,578,699,-1,898,294,-1,575,168,432,833],[427,-1,-1,-1,366,-1,-1,635,-1,32,962,468,893,854,718,427,448,916,258,-1,760,909,529,311,404,-1,-1,588,680,875,-1,615,-1,409,758,221,-1,-1,76,257],[668,-1,926,366,-1,-1,-1,250,268,-1,503,944,-1,677,-1,727,793,457,981,191,-1,-1,-1,351,969,925,987,328,282,589,-1,873,477,-1,-1,19,450,-1,-1,-1],[495,508,-1,-1,-1,-1,-1,765,711,819,305,302,926,-1,-1,582,-1,861,-1,683,293,-1,-1,66,-1,27,-1,-1,290,-1,786,-1,554,817,33,-1,54,506,386,381],[377,472,958,-1,-1,-1,-1,-1,-1,120,42,-1,134,219,457,639,538,374,-1,-1,-1,966,-1,-1,-1,-1,-1,449,120,797,358,232,550,-1,305,997,662,744,686,239],[678,799,158,635,250,765,-1,-1,-1,35,-1,106,385,652,160,-1,890,812,605,953,-1,-1,-1,79,-1,712,613,312,452,-1,978,900,-1,901,-1,-1,225,533,770,722],[-1,-1,647,-1,268,711,-1,-1,-1,283,-1,172,-1,663,236,36,403,286,986,-1,-1,810,761,574,53,793,-1,-1,777,330,936,883,286,-1,174,-1,-1,-1,828,711],[177,956,47,32,-1,819,120,35,283,-1,50,-1,565,36,767,684,344,489,565,-1,-1,103,810,463,733,665,494,644,863,25,385,-1,342,470,-1,-1,-1,730,582,468],[-1,578,621,962,503,305,42,-1,-1,50,-1,155,519,-1,-1,256,990,801,154,53,474,650,402,-1,-1,-1,966,-1,-1,406,989,772,932,7,-1,823,391,-1,-1,933],[-1,363,264,468,944,302,-1,106,172,-1,155,-1,-1,-1,380,438,-1,41,266,-1,-1,104,867,609,-1,270,861,-1,-1,165,-1,675,250,686,995,366,191,-1,433,-1],[870,940,81,893,-1,926,134,385,-1,565,519,-1,-1,313,851,-1,-1,-1,248,220,-1,826,359,829,-1,234,198,145,409,68,359,-1,814,218,186,-1,-1,929,203,-1],[-1,143,-1,854,677,-1,219,652,663,36,-1,-1,313,-1,132,-1,433,598,-1,-1,168,870,-1,-1,-1,128,437,-1,383,364,966,227,-1,-1,807,993,-1,-1,526,17],[869,-1,402,718,-1,-1,457,160,236,767,-1,380,851,132,-1,-1,596,903,613,730,-1,261,-1,142,379,885,89,-1,848,258,112,-1,900,-1,-1,818,639,268,600,-1],[624,162,813,427,727,582,639,-1,36,684,256,438,-1,-1,-1,-1,539,379,664,561,542,-1,999,585,-1,-1,321,398,-1,-1,950,68,193,-1,697,-1,390,588,848,-1],[300,122,649,448,793,-1,538,890,403,344,990,-1,-1,433,596,539,-1,-1,73,-1,318,-1,-1,500,-1,968,-1,291,-1,-1,765,196,504,757,-1,542,-1,395,227,148],[609,910,386,916,457,861,374,812,286,489,801,41,-1,598,903,379,-1,-1,-1,946,136,399,-1,941,707,156,757,258,251,-1,807,-1,-1,-1,461,501,-1,-1,616,-1],[131,-1,252,258,981,-1,-1,605,986,565,154,266,248,-1,613,664,73,-1,-1,686,-1,-1,575,627,817,282,-1,698,398,222,-1,649,-1,-1,-1,-1,-1,654,-1,-1],[-1,729,391,-1,191,683,-1,953,-1,-1,53,-1,220,-1,730,561,-1,946,686,-1,-1,389,729,553,304,703,455,857,260,-1,991,182,351,477,867,-1,-1,889,217,853],[251,802,264,760,-1,293,-1,-1,-1,-1,474,-1,-1,168,-1,542,318,136,-1,-1,-1,-1,392,-1,-1,-1,267,407,27,651,80,927,-1,974,977,-1,-1,457,117,-1],[-1,941,637,909,-1,-1,966,-1,810,103,650,104,826,870,261,-1,-1,399,-1,389,-1,-1,-1,202,-1,-1,-1,-1,867,140,403,962,785,-1,511,-1,1,-1,707,-1],[-1,922,349,529,-1,-1,-1,-1,761,810,402,867,359,-1,-1,999,-1,-1,575,729,392,-1,-1,388,939,-1,959,-1,83,463,361,-1,-1,512,931,-1,224,690,369,-1],[-1,573,-1,311,351,66,-1,79,574,463,-1,609,829,-1,142,585,500,941,627,553,-1,202,388,-1,164,829,-1,620,523,639,936,-1,-1,490,-1,695,-1,505,109,-1],[856,531,-1,404,969,-1,-1,-1,53,733,-1,-1,-1,-1,379,-1,-1,707,817,304,-1,-1,939,164,-1,-1,616,716,728,-1,889,349,-1,963,150,447,-1,292,586,264],[221,539,-1,-1,925,27,-1,712,793,665,-1,270,234,128,885,-1,968,156,282,703,-1,-1,-1,829,-1,-1,-1,822,-1,-1,-1,736,576,-1,697,946,443,-1,205,194],[514,667,108,-1,987,-1,-1,613,-1,494,966,861,198,437,89,321,-1,757,-1,455,267,-1,959,-1,616,-1,-1,-1,349,156,339,-1,102,790,359,-1,439,938,809,260],[-1,607,-1,588,328,-1,449,312,-1,644,-1,-1,145,-1,-1,398,291,258,698,857,407,-1,-1,620,716,822,-1,-1,293,486,943,-1,779,-1,6,880,116,775,-1,947],[591,-1,727,680,282,290,120,452,777,863,-1,-1,409,383,848,-1,-1,251,398,260,27,867,83,523,728,-1,349,293,-1,212,684,505,341,384,9,992,507,48,-1,-1],[762,920,225,875,589,-1,797,-1,330,25,406,165,68,364,258,-1,-1,-1,222,-1,651,140,463,639,-1,-1,156,486,212,-1,-1,349,723,-1,-1,186,-1,36,240,752],[182,-1,578,-1,-1,786,358,978,936,385,989,-1,359,966,112,950,765,807,-1,991,80,403,361,936,889,-1,339,943,684,-1,-1,965,302,676,725,-1,327,134,-1,147],[56,-1,699,615,873,-1,232,900,883,-1,772,675,-1,227,-1,68,196,-1,649,182,927,962,-1,-1,349,736,-1,-1,505,349,965,-1,474,178,833,-1,-1,555,853,-1],[-1,315,-1,-1,477,554,550,-1,286,342,932,250,814,-1,900,193,504,-1,-1,351,-1,785,-1,-1,-1,576,102,779,341,723,302,474,-1,689,-1,-1,-1,451,-1,-1],[884,649,898,409,-1,817,-1,901,-1,470,7,686,218,-1,-1,-1,757,-1,-1,477,974,-1,512,490,963,-1,790,-1,384,-1,676,178,689,-1,245,596,445,-1,-1,343],[412,937,294,758,-1,33,305,-1,174,-1,-1,995,186,807,-1,697,-1,461,-1,867,977,511,931,-1,150,697,359,6,9,-1,725,833,-1,245,-1,949,-1,270,-1,112],[273,-1,-1,221,19,-1,997,-1,-1,-1,823,366,-1,993,818,-1,542,501,-1,-1,-1,-1,-1,695,447,946,-1,880,992,186,-1,-1,-1,596,949,-1,91,-1,768,273],[636,185,575,-1,450,54,662,225,-1,-1,391,191,-1,-1,639,390,-1,-1,-1,-1,-1,1,224,-1,-1,443,439,116,507,-1,327,-1,-1,445,-1,91,-1,248,-1,344],[-1,102,168,-1,-1,506,744,533,-1,730,-1,-1,929,-1,268,588,395,-1,654,889,457,-1,690,505,292,-1,938,775,48,36,134,555,451,-1,270,-1,248,-1,371,680],[-1,636,432,76,-1,386,686,770,828,582,-1,433,203,526,600,848,227,616,-1,217,117,707,369,109,586,205,809,-1,-1,240,-1,853,-1,-1,-1,768,-1,371,-1,540],[774,289,833,257,-1,381,239,722,711,468,933,-1,-1,17,-1,-1,148,-1,-1,853,-1,-1,-1,-1,264,194,260,947,-1,752,147,-1,-1,343,112,273,344,680,540,-1]
];
```

## --seed-contents--

```js
function minimalNetwork(network) {

  return true;
}

const testNetwork = [
  [-1,-1,-1,427,668,495,377,678,-1,177,-1,-1,870,-1,869,624,300,609,131,-1,251,-1,-1,-1,856,221,514,-1,591,762,182,56,-1,884,412,273,636,-1,-1,774],[-1,-1,262,-1,-1,508,472,799,-1,956,578,363,940,143,-1,162,122,910,-1,729,802,941,922,573,531,539,667,607,-1,920,-1,-1,315,649,937,-1,185,102,636,289],[-1,262,-1,-1,926,-1,958,158,647,47,621,264,81,-1,402,813,649,386,252,391,264,637,349,-1,-1,-1,108,-1,727,225,578,699,-1,898,294,-1,575,168,432,833],[427,-1,-1,-1,366,-1,-1,635,-1,32,962,468,893,854,718,427,448,916,258,-1,760,909,529,311,404,-1,-1,588,680,875,-1,615,-1,409,758,221,-1,-1,76,257],[668,-1,926,366,-1,-1,-1,250,268,-1,503,944,-1,677,-1,727,793,457,981,191,-1,-1,-1,351,969,925,987,328,282,589,-1,873,477,-1,-1,19,450,-1,-1,-1],[495,508,-1,-1,-1,-1,-1,765,711,819,305,302,926,-1,-1,582,-1,861,-1,683,293,-1,-1,66,-1,27,-1,-1,290,-1,786,-1,554,817,33,-1,54,506,386,381],[377,472,958,-1,-1,-1,-1,-1,-1,120,42,-1,134,219,457,639,538,374,-1,-1,-1,966,-1,-1,-1,-1,-1,449,120,797,358,232,550,-1,305,997,662,744,686,239],[678,799,158,635,250,765,-1,-1,-1,35,-1,106,385,652,160,-1,890,812,605,953,-1,-1,-1,79,-1,712,613,312,452,-1,978,900,-1,901,-1,-1,225,533,770,722],[-1,-1,647,-1,268,711,-1,-1,-1,283,-1,172,-1,663,236,36,403,286,986,-1,-1,810,761,574,53,793,-1,-1,777,330,936,883,286,-1,174,-1,-1,-1,828,711],[177,956,47,32,-1,819,120,35,283,-1,50,-1,565,36,767,684,344,489,565,-1,-1,103,810,463,733,665,494,644,863,25,385,-1,342,470,-1,-1,-1,730,582,468],[-1,578,621,962,503,305,42,-1,-1,50,-1,155,519,-1,-1,256,990,801,154,53,474,650,402,-1,-1,-1,966,-1,-1,406,989,772,932,7,-1,823,391,-1,-1,933],[-1,363,264,468,944,302,-1,106,172,-1,155,-1,-1,-1,380,438,-1,41,266,-1,-1,104,867,609,-1,270,861,-1,-1,165,-1,675,250,686,995,366,191,-1,433,-1],[870,940,81,893,-1,926,134,385,-1,565,519,-1,-1,313,851,-1,-1,-1,248,220,-1,826,359,829,-1,234,198,145,409,68,359,-1,814,218,186,-1,-1,929,203,-1],[-1,143,-1,854,677,-1,219,652,663,36,-1,-1,313,-1,132,-1,433,598,-1,-1,168,870,-1,-1,-1,128,437,-1,383,364,966,227,-1,-1,807,993,-1,-1,526,17],[869,-1,402,718,-1,-1,457,160,236,767,-1,380,851,132,-1,-1,596,903,613,730,-1,261,-1,142,379,885,89,-1,848,258,112,-1,900,-1,-1,818,639,268,600,-1],[624,162,813,427,727,582,639,-1,36,684,256,438,-1,-1,-1,-1,539,379,664,561,542,-1,999,585,-1,-1,321,398,-1,-1,950,68,193,-1,697,-1,390,588,848,-1],[300,122,649,448,793,-1,538,890,403,344,990,-1,-1,433,596,539,-1,-1,73,-1,318,-1,-1,500,-1,968,-1,291,-1,-1,765,196,504,757,-1,542,-1,395,227,148],[609,910,386,916,457,861,374,812,286,489,801,41,-1,598,903,379,-1,-1,-1,946,136,399,-1,941,707,156,757,258,251,-1,807,-1,-1,-1,461,501,-1,-1,616,-1],[131,-1,252,258,981,-1,-1,605,986,565,154,266,248,-1,613,664,73,-1,-1,686,-1,-1,575,627,817,282,-1,698,398,222,-1,649,-1,-1,-1,-1,-1,654,-1,-1],[-1,729,391,-1,191,683,-1,953,-1,-1,53,-1,220,-1,730,561,-1,946,686,-1,-1,389,729,553,304,703,455,857,260,-1,991,182,351,477,867,-1,-1,889,217,853],[251,802,264,760,-1,293,-1,-1,-1,-1,474,-1,-1,168,-1,542,318,136,-1,-1,-1,-1,392,-1,-1,-1,267,407,27,651,80,927,-1,974,977,-1,-1,457,117,-1],[-1,941,637,909,-1,-1,966,-1,810,103,650,104,826,870,261,-1,-1,399,-1,389,-1,-1,-1,202,-1,-1,-1,-1,867,140,403,962,785,-1,511,-1,1,-1,707,-1],[-1,922,349,529,-1,-1,-1,-1,761,810,402,867,359,-1,-1,999,-1,-1,575,729,392,-1,-1,388,939,-1,959,-1,83,463,361,-1,-1,512,931,-1,224,690,369,-1],[-1,573,-1,311,351,66,-1,79,574,463,-1,609,829,-1,142,585,500,941,627,553,-1,202,388,-1,164,829,-1,620,523,639,936,-1,-1,490,-1,695,-1,505,109,-1],[856,531,-1,404,969,-1,-1,-1,53,733,-1,-1,-1,-1,379,-1,-1,707,817,304,-1,-1,939,164,-1,-1,616,716,728,-1,889,349,-1,963,150,447,-1,292,586,264],[221,539,-1,-1,925,27,-1,712,793,665,-1,270,234,128,885,-1,968,156,282,703,-1,-1,-1,829,-1,-1,-1,822,-1,-1,-1,736,576,-1,697,946,443,-1,205,194],[514,667,108,-1,987,-1,-1,613,-1,494,966,861,198,437,89,321,-1,757,-1,455,267,-1,959,-1,616,-1,-1,-1,349,156,339,-1,102,790,359,-1,439,938,809,260],[-1,607,-1,588,328,-1,449,312,-1,644,-1,-1,145,-1,-1,398,291,258,698,857,407,-1,-1,620,716,822,-1,-1,293,486,943,-1,779,-1,6,880,116,775,-1,947],[591,-1,727,680,282,290,120,452,777,863,-1,-1,409,383,848,-1,-1,251,398,260,27,867,83,523,728,-1,349,293,-1,212,684,505,341,384,9,992,507,48,-1,-1],[762,920,225,875,589,-1,797,-1,330,25,406,165,68,364,258,-1,-1,-1,222,-1,651,140,463,639,-1,-1,156,486,212,-1,-1,349,723,-1,-1,186,-1,36,240,752],[182,-1,578,-1,-1,786,358,978,936,385,989,-1,359,966,112,950,765,807,-1,991,80,403,361,936,889,-1,339,943,684,-1,-1,965,302,676,725,-1,327,134,-1,147],[56,-1,699,615,873,-1,232,900,883,-1,772,675,-1,227,-1,68,196,-1,649,182,927,962,-1,-1,349,736,-1,-1,505,349,965,-1,474,178,833,-1,-1,555,853,-1],[-1,315,-1,-1,477,554,550,-1,286,342,932,250,814,-1,900,193,504,-1,-1,351,-1,785,-1,-1,-1,576,102,779,341,723,302,474,-1,689,-1,-1,-1,451,-1,-1],[884,649,898,409,-1,817,-1,901,-1,470,7,686,218,-1,-1,-1,757,-1,-1,477,974,-1,512,490,963,-1,790,-1,384,-1,676,178,689,-1,245,596,445,-1,-1,343],[412,937,294,758,-1,33,305,-1,174,-1,-1,995,186,807,-1,697,-1,461,-1,867,977,511,931,-1,150,697,359,6,9,-1,725,833,-1,245,-1,949,-1,270,-1,112],[273,-1,-1,221,19,-1,997,-1,-1,-1,823,366,-1,993,818,-1,542,501,-1,-1,-1,-1,-1,695,447,946,-1,880,992,186,-1,-1,-1,596,949,-1,91,-1,768,273],[636,185,575,-1,450,54,662,225,-1,-1,391,191,-1,-1,639,390,-1,-1,-1,-1,-1,1,224,-1,-1,443,439,116,507,-1,327,-1,-1,445,-1,91,-1,248,-1,344],[-1,102,168,-1,-1,506,744,533,-1,730,-1,-1,929,-1,268,588,395,-1,654,889,457,-1,690,505,292,-1,938,775,48,36,134,555,451,-1,270,-1,248,-1,371,680],[-1,636,432,76,-1,386,686,770,828,582,-1,433,203,526,600,848,227,616,-1,217,117,707,369,109,586,205,809,-1,-1,240,-1,853,-1,-1,-1,768,-1,371,-1,540],[774,289,833,257,-1,381,239,722,711,468,933,-1,-1,17,-1,-1,148,-1,-1,853,-1,-1,-1,-1,264,194,260,947,-1,752,147,-1,-1,343,112,273,344,680,540,-1]
];

minimalNetwork(testNetwork);
```

# --solutions--

```js
// solution required
```
