The net is not the important thing, but that of what is gathered in the net that needs to be separated as good or evil, wheat and tares, sheep from the goats. Other words those here on earth that are either God's own, or those who have rejected Him.
A good cross reference for Matthew 13:47 would be the parable found in Matthew 13:24-30, Matthew 22:1-14; and Matthew 25:31-46. These are about separating the good (those who are Christ own) from those who have not Christ when Jesus returns and separates the sheep from the goats