Identifying　the　essential　characteristics　and　forecasting　carbon　prices　is　significant　in　promoting　green　transformation.　This　study　transforms　the　time　series　into　networks　based　on　China＇s　pilots　by　using　the　visibility　graph,　mining　more　information　on　the　structure　features.　Then,　we　calculate　nodes＇　similarity　to　forecast　the　carbon　prices　by　link　prediction.　To　improve　the　predicted　accuracy,　we　notice　the　node　distance　to　introduce　the　weight　coefficient,　measuring　the　impact　of　different　nodes　on　future　nodes.　Finally,　this　study　divides　eight　pilots　into　different　communities　by　hierarchical　clustering　to　study　the　similarities　between　these　pilots.　The　results　show　that　eight　pilots　are　the　＂small　world　＂　networks　except　for　Chongqing　and　Shenzhen　pilots,　all　of　which　are　＂scale-free　＂　networks　except　for　Shanghai　and　Tianjin　pilots.　Compared　with　other　predicted　methods,　the　proposed　method　in　this　study　has　good　predicted　performance.　Moreover,　these　eight　pilots　are　divided　into　three　clusters,　indicating　a　higher　similarity　in　their　price-setting　schemes　in　the　same　community.　Based　on　the　analysis　of　China＇s　pilots,　this　study　provides　references　for　carbon　trading　and　related　enterprises.