Urban　air　quality　is　related　to　human　health　in　modern　life.　The　statistical　features　of　urban　air　quality　highly　depend　on　the　division　of　historical　stages.　Conventional　division　methods　that　use　a　fixed　period　(e.g.,　month)　can　result　in　confusion　during　statistical　analysis.　In　this　study,　we　propose　a　novel　analysis　technique　based　on　time　series　complex　network　theories　to　divide　the　historical　information　of　urban　air　quality　by　using　flexible　periods.　First,　air　quality　information　is　converted　into　time　series　complex　networks　via　a　multilayer　visibility　model.　Thereafter,　an　improved　community　detection　algorithm　is　proposed　on　the　basis　of　network　characteristics.　In　particular,　the　centrality　of　nodes　is　increased　using　a　kernel　density　estimation　model.　An　improved　bidirectional　search　pattern　results　in　the　optimal　modularity.　Finally,　the　historical　curves　of　urban　air　quality　are　divided　into　several　stages　in　accordance　with　the　optimal　clustering　results.　The　simulation　experiments　demonstrate　important　conclusions.　The　clustering　accuracy　of　the　proposed　algorithm　is　superior　to　those　of　other　evaluated　methods　on　actual　air　quality　networks.　The　number　of　historical　stages　is　decreased　constantly　in　accordance　with　clustering　results,　and　this　condition　is　beneficial　for　statistics.　Our　results　can　reasonably　explain　the　relationship　between　valid　time　and　air　quality　features.　The　proposed　technique　can　provide　effective　and　reliable　division　results　of　historical　stages.　(c)　2021　Elsevier　Inc.　All　rights　reserved.