The team was selected by a national panel of 50 media members. Guard Jahri Evans made the second team.
Graham was one vote away from being a unanimous selection.
Graham finished the 2013 regular season with 16 touchdown receptions, a franchise record and second-most by a tight end in NFL history behind only Rob Gronkowski, who caught 17 TD passes for the Patriots in 2011.
Graham also had a team-leading 86 receptions for 1,215 yards.
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