Collaborative　filtering　(CF)　is　the　dominant　technique　in　personalized　recommendation.　It　models　user-item　interactions　to　select　the　relevant　items　for　a　user,　and　it　is　widely　applied　in　real　recommender　systems.　Recently,　graph　convolutional　network　(GCN)　has　been　incorporated　into　CF,　and　it　achieves　better　performance　in　many　recommendation　scenarios.　However,　existing　works　usually　suffer　from　limited　performance　due　to　data　sparsity　and　high　computational　costs　in　large　user-item　graphs.　In　this　paper,　we　propose　a　linear　graph　convolutional　CF　(LGCCF)　framework　that　incorporates　the　social　influence　as　side　information　to　help　improve　recommendation　and　address　the　aforementioned　issues.　Specifically,　LGCCF　integrates　the　user-item　interactions　and　the　social　influence　into　a　unified　GCN　model　to　alleviate　data　sparsity.　Furthermore,　in　the　graph　convolutional　operations　of　LGCCF,　we　remove　the　nonlinear　transformations　and　replace　them　with　linear　embedding　propagations　to　overcome　training　difficulty　and　improve　the　recommendation　performance.　Finally,　extensive　experiments　conducted　on　two　real　datasets　show　that　LGCCF　consistently　outperforms　the　state-of-the-art　recommendation　methods.　©　2021,　Springer　Nature　Switzerland　AG.