Emergency　control　is　essential　for　maintaining　the　stability　of　power　systems,　serving　as　a　key　defense　mechanism　against　the　destabilization　and　cascading　failures　triggered　by　faults.　Under-voltage　load　shedding　is　a　popular　and　effective　approach　for　emergency　control.　However,　with　the　increasing　complexity　and　scale　of　power　systems　and　the　rise　in　uncertainty　factors,　traditional　approaches　struggle　with　computation　speed,　accuracy,　and　scalability　issues.　Deep　reinforcement　learning　holds　significant　potential　for　the　power　system　decision-making　problems.　However,　existing　deep　reinforcement　learning　algorithms　have　limitations　in　effectively　leveraging　diverse　operational　features,　which　affects　the　reliability　and　efficiency　of　emergency　control　strategies.　This　paper　presents　an　innovative　approach　for　real-time　emergency　voltage　control　strategies　for　transient　stability　enhancement　through　the　integration　of　edge-graph　convolutional　networks　with　reinforcement　learning.　This　method　transforms　the　traditional　emergency　control　optimization　problem　into　a　sequential　decision-making　process.　By　utilizing　the　edge-graph　convolutional　neural　network,　it　efficiently　extracts　critical　information　on　the　correlation　between　the　power　system　operation　status　and　node　branch　information,　as　well　as　the　uncertainty　factors　involved.　Moreover,　the　clipped　double　Q-learning,　delayed　policy　update,　and　target　policy　smoothing　are　introduced　to　effectively　solve　the　issues　of　overestimation　and　abnormal　sensitivity　to　hyperparameters　in　the　deep　deterministic　policy　gradient　algorithm.　The　effectiveness　of　the　proposed　method　in　emergency　control　decision-making　is　verified　by　the　IEEE　39-bus　system　and　the　IEEE　118-bus　system.