Multi-energy　flow　calculation　is　the　foundation　for　integrated　energy　system　analysis　and　optimal　operation.　In　the　context　of　limited　interaction　information　among　network　operation　entities,　a　novel　recursive　electricity-gas-heat　multi-energy　flow　algorithm　is　proposed.　The　proposed　algorithm　is　based　on　the　bidirectional　transmission　of　power　series　coefficients,　aims　to　boost　both　convergence　and　computational　efficiency.　First,　the　holomorphic　embedding　energy　flow　models　of　electricity,　gas,　and　heat　energy　systems　are　established　respectively.　Second,　the　recursive　solver　principle　of　the　holomorphic　embedding　method　in　multi-energy　flow　calculation　is　analyzed.　It　notes　that　the　transmission　of　power　series　coefficients　can　be　divided　into　two　categories:　horizontal　transmission　and　vertical　transmission.　Therefore,　a　holomorphic　embedding　multi-energy　flow　model　that　can　be　solved　by　bidirectional　transmission　is　established.　Subsequently,　the　recursive　relationship　for　the　coefficients　of　the　power　series　in　each　holomorphic　embedding　state　quantity　is　derived.　The　power　series　coefficients　of　each　state　quantity　to　be　solved　are　recursively　obtained　through　bidirectional　transmission,　enabling　the　joint　solution　of　electricity-gas-heat　multi-energy　flow.　Finally,　the　results　demonstrate　the　feasibility　of　the　proposed　algorithm.　The　proposed　algorithm　calculates　the　multi-energy　flow　based　on　a　small　amount　of　interaction　information　with　better　convergence　and　computational　efficiency.　©　2024　Power　System　Technology　Press.　All　rights　reserved.