Contagion　(spread　of　harmful　idea)　and　control　of　bank　risk　have　been　an　eternal　topic　in　the　field　of　financial　research.　In　this　paper,　we　firstly　use　the　savings　mechanism　to　combine　the　social　network　of　depositors　with　the　network　of　balance　sheets　in　the　banking　system　to　build　multiple　networks　for　the　banking　industry.　Secondly,　aiming　at　the　heterogeneity　of　depositors,　construct　an　improved　SIS　model　based　on　node　attitudes　to　represent　the　decision-making　process　of　a　bank　run　during　the　spread　of　panic　emotions　in　social　networks.　Finally,　three　sets　of　simulation　experiments　were　designed　using　a　multi-agent　model　to　analyse　the　interaction　between　bank　risk　contagion　and　depositor　panic　contagion　under　initial　asset　shocks,　the　sensitivity　of　two　types　of　risk　contagion,　and　bank　risk　contagion　under　initial　rumour　shocks.　Results　show　that:　(i)　The　contagion　of　bank　risks　and　the　spread　of　panic　emotions　of　depositors　will　affect　each　other,　which　will　further　expand　the　scope　of　the　spread　of　bank　risk　and　panic　emotions;　(ii)　depositors　in　social　networks　are　more　likely　to　be　affected　by　the　negative　emotions　around　them;　(iii)　The　key　to　stabilizing　the　banking　system,　while　sufficient　liquidity　can　effectively　help　the　banking　system　resist　rumour　attacks.　©　2021　John　Wiley　&　Sons,　Ltd.