How many possible routes are there for this problem if it is constructed as a network model? Distances between cities are given in miles.

Matrix of Distances Between Cities in Miles

$\backslash$table$[[,$I,$1,2,3,4,5,1,6,7,8],[1$ Philadelphia PA$,$I,,$981,2409,672,1150,$I,$738,1046,988],[2$ Des Moines IA$,$I,$981,,1442,312,174,$i$,256,177,238],[3$ Los Angeles CA$,$I,$2409,1442,,1752,1268,$I,$1673,1364,1531],[4$ Chicago IL$,$I,$672,312,1752,,484,1,119,414,353],[5$ Lincoln NE$,$I,$1150,174,1268,484,,$I,$415,167,343],[6$ Bloomington IL$,$I,$738,256,1673,119,415,1,,315,380],[7$ Kansas City KS$,$I,$1046,177,1364,414,167,$i$,315,,413],[8$ Minneapolis $MN,$I,$988,238,1531,353,343,$i$,380,413,]]$