mat={{∞,16,12,21,∞,∞,∞},{16,∞,∞,17,20,∞,∞},{12,∞,∞,28,∞,31,∞},{21,17,28,∞,18,19,23},{∞,20,∞,18,∞,∞,11},{∞,∞,31,19,∞,∞,27},{∞,∞,∞,23,11,27,∞}};

g=WeightedAdjacencyGraph[mat];

Graph[g,EdgeLabels->"EdgeWeight"]

s=FindSpanningTree[g]

HighlightGraph[g,s]

Graph[s,EdgeLabels->"EdgeWeight"]

(* https://mathematica.stackexchange.com/questions/4221/how-to-extract-edgeweights-from-a-graph *)

SumOfWeights[g_]:=Total[Map[#[[2]]&,Map[{#,PropertyValue[{g,#},EdgeWeight]}&,EdgeList[g]]]]

SumOfWeights[g]-SumOfWeights[s]

mat2={{∞,∞,∞,427,668,495,377,678,∞,177,∞,∞,870,∞,869,624,300,609,131,∞,251,∞,∞,∞,856,221,514,∞,591,762,182,56,∞,884,412,273,636,∞,∞,774},{∞,∞,262,∞,∞,508,472,799,∞,956,578,363,940,143,∞,162,122,910,∞,729,802,941,922,573,531,539,667,607,∞,920,∞,∞,315,649,937,∞,185,102,636,289},{∞,262,∞,∞,926,∞,958,158,647,47,621,264,81,∞,402,813,649,386,252,391,264,637,349,∞,∞,∞,108,∞,727,225,578,699,∞,898,294,∞,575,168,432,833},{427,∞,∞,∞,366,∞,∞,635,∞,32,962,468,893,854,718,427,448,916,258,∞,760,909,529,311,404,∞,∞,588,680,875,∞,615,∞,409,758,221,∞,∞,76,257},{668,∞,926,366,∞,∞,∞,250,268,∞,503,944,∞,677,∞,727,793,457,981,191,∞,∞,∞,351,969,925,987,328,282,589,∞,873,477,∞,∞,19,450,∞,∞,∞},{495,508,∞,∞,∞,∞,∞,765,711,819,305,302,926,∞,∞,582,∞,861,∞,683,293,∞,∞,66,∞,27,∞,∞,290,∞,786,∞,554,817,33,∞,54,506,386,381},{377,472,958,∞,∞,∞,∞,∞,∞,120,42,∞,134,219,457,639,538,374,∞,∞,∞,966,∞,∞,∞,∞,∞,449,120,797,358,232,550,∞,305,997,662,744,686,239},{678,799,158,635,250,765,∞,∞,∞,35,∞,106,385,652,160,∞,890,812,605,953,∞,∞,∞,79,∞,712,613,312,452,∞,978,900,∞,901,∞,∞,225,533,770,722},{∞,∞,647,∞,268,711,∞,∞,∞,283,∞,172,∞,663,236,36,403,286,986,∞,∞,810,761,574,53,793,∞,∞,777,330,936,883,286,∞,174,∞,∞,∞,828,711},{177,956,47,32,∞,819,120,35,283,∞,50,∞,565,36,767,684,344,489,565,∞,∞,103,810,463,733,665,494,644,863,25,385,∞,342,470,∞,∞,∞,730,582,468},{∞,578,621,962,503,305,42,∞,∞,50,∞,155,519,∞,∞,256,990,801,154,53,474,650,402,∞,∞,∞,966,∞,∞,406,989,772,932,7,∞,823,391,∞,∞,933},{∞,363,264,468,944,302,∞,106,172,∞,155,∞,∞,∞,380,438,∞,41,266,∞,∞,104,867,609,∞,270,861,∞,∞,165,∞,675,250,686,995,366,191,∞,433,∞},{870,940,81,893,∞,926,134,385,∞,565,519,∞,∞,313,851,∞,∞,∞,248,220,∞,826,359,829,∞,234,198,145,409,68,359,∞,814,218,186,∞,∞,929,203,∞},{∞,143,∞,854,677,∞,219,652,663,36,∞,∞,313,∞,132,∞,433,598,∞,∞,168,870,∞,∞,∞,128,437,∞,383,364,966,227,∞,∞,807,993,∞,∞,526,17},{869,∞,402,718,∞,∞,457,160,236,767,∞,380,851,132,∞,∞,596,903,613,730,∞,261,∞,142,379,885,89,∞,848,258,112,∞,900,∞,∞,818,639,268,600,∞},{624,162,813,427,727,582,639,∞,36,684,256,438,∞,∞,∞,∞,539,379,664,561,542,∞,999,585,∞,∞,321,398,∞,∞,950,68,193,∞,697,∞,390,588,848,∞},{300,122,649,448,793,∞,538,890,403,344,990,∞,∞,433,596,539,∞,∞,73,∞,318,∞,∞,500,∞,968,∞,291,∞,∞,765,196,504,757,∞,542,∞,395,227,148},{609,910,386,916,457,861,374,812,286,489,801,41,∞,598,903,379,∞,∞,∞,946,136,399,∞,941,707,156,757,258,251,∞,807,∞,∞,∞,461,501,∞,∞,616,∞},{131,∞,252,258,981,∞,∞,605,986,565,154,266,248,∞,613,664,73,∞,∞,686,∞,∞,575,627,817,282,∞,698,398,222,∞,649,∞,∞,∞,∞,∞,654,∞,∞},{∞,729,391,∞,191,683,∞,953,∞,∞,53,∞,220,∞,730,561,∞,946,686,∞,∞,389,729,553,304,703,455,857,260,∞,991,182,351,477,867,∞,∞,889,217,853},{251,802,264,760,∞,293,∞,∞,∞,∞,474,∞,∞,168,∞,542,318,136,∞,∞,∞,∞,392,∞,∞,∞,267,407,27,651,80,927,∞,974,977,∞,∞,457,117,∞},{∞,941,637,909,∞,∞,966,∞,810,103,650,104,826,870,261,∞,∞,399,∞,389,∞,∞,∞,202,∞,∞,∞,∞,867,140,403,962,785,∞,511,∞,1,∞,707,∞},{∞,922,349,529,∞,∞,∞,∞,761,810,402,867,359,∞,∞,999,∞,∞,575,729,392,∞,∞,388,939,∞,959,∞,83,463,361,∞,∞,512,931,∞,224,690,369,∞},{∞,573,∞,311,351,66,∞,79,574,463,∞,609,829,∞,142,585,500,941,627,553,∞,202,388,∞,164,829,∞,620,523,639,936,∞,∞,490,∞,695,∞,505,109,∞},{856,531,∞,404,969,∞,∞,∞,53,733,∞,∞,∞,∞,379,∞,∞,707,817,304,∞,∞,939,164,∞,∞,616,716,728,∞,889,349,∞,963,150,447,∞,292,586,264},{221,539,∞,∞,925,27,∞,712,793,665,∞,270,234,128,885,∞,968,156,282,703,∞,∞,∞,829,∞,∞,∞,822,∞,∞,∞,736,576,∞,697,946,443,∞,205,194},{514,667,108,∞,987,∞,∞,613,∞,494,966,861,198,437,89,321,∞,757,∞,455,267,∞,959,∞,616,∞,∞,∞,349,156,339,∞,102,790,359,∞,439,938,809,260},{∞,607,∞,588,328,∞,449,312,∞,644,∞,∞,145,∞,∞,398,291,258,698,857,407,∞,∞,620,716,822,∞,∞,293,486,943,∞,779,∞,6,880,116,775,∞,947},{591,∞,727,680,282,290,120,452,777,863,∞,∞,409,383,848,∞,∞,251,398,260,27,867,83,523,728,∞,349,293,∞,212,684,505,341,384,9,992,507,48,∞,∞},{762,920,225,875,589,∞,797,∞,330,25,406,165,68,364,258,∞,∞,∞,222,∞,651,140,463,639,∞,∞,156,486,212,∞,∞,349,723,∞,∞,186,∞,36,240,752},{182,∞,578,∞,∞,786,358,978,936,385,989,∞,359,966,112,950,765,807,∞,991,80,403,361,936,889,∞,339,943,684,∞,∞,965,302,676,725,∞,327,134,∞,147},{56,∞,699,615,873,∞,232,900,883,∞,772,675,∞,227,∞,68,196,∞,649,182,927,962,∞,∞,349,736,∞,∞,505,349,965,∞,474,178,833,∞,∞,555,853,∞},{∞,315,∞,∞,477,554,550,∞,286,342,932,250,814,∞,900,193,504,∞,∞,351,∞,785,∞,∞,∞,576,102,779,341,723,302,474,∞,689,∞,∞,∞,451,∞,∞},{884,649,898,409,∞,817,∞,901,∞,470,7,686,218,∞,∞,∞,757,∞,∞,477,974,∞,512,490,963,∞,790,∞,384,∞,676,178,689,∞,245,596,445,∞,∞,343},{412,937,294,758,∞,33,305,∞,174,∞,∞,995,186,807,∞,697,∞,461,∞,867,977,511,931,∞,150,697,359,6,9,∞,725,833,∞,245,∞,949,∞,270,∞,112},{273,∞,∞,221,19,∞,997,∞,∞,∞,823,366,∞,993,818,∞,542,501,∞,∞,∞,∞,∞,695,447,946,∞,880,992,186,∞,∞,∞,596,949,∞,91,∞,768,273},{636,185,575,∞,450,54,662,225,∞,∞,391,191,∞,∞,639,390,∞,∞,∞,∞,∞,1,224,∞,∞,443,439,116,507,∞,327,∞,∞,445,∞,91,∞,248,∞,344},{∞,102,168,∞,∞,506,744,533,∞,730,∞,∞,929,∞,268,588,395,∞,654,889,457,∞,690,505,292,∞,938,775,48,36,134,555,451,∞,270,∞,248,∞,371,680},{∞,636,432,76,∞,386,686,770,828,582,∞,433,203,526,600,848,227,616,∞,217,117,707,369,109,586,205,809,∞,∞,240,∞,853,∞,∞,∞,768,∞,371,∞,540},{774,289,833,257,∞,381,239,722,711,468,933,∞,∞,17,∞,∞,148,∞,∞,853,∞,∞,∞,∞,264,194,260,947,∞,752,147,∞,∞,343,112,273,344,680,540,∞}};

g2=WeightedAdjacencyGraph[mat2];

s2=FindSpanningTree[g2];

SumOfWeights[g2]-SumOfWeights[s2]