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In this paper, we propose a novel GNN (called Graph in Graph Neural (GIG) Network) which can process graph-style data (called GIG sample) whose vertices are further represented by graphs. Given a set of graphs or a data sample whose components can be represented by a set of graphs (called multi-graph data sample), our GIG network starts with a GIG sample generation (GSG) module which encodes the input as a\n                    <jats:bold>GIG sample<\/jats:bold>\n                    , where each GIG vertex includes a graph. Then, a set of GIG hidden layers are stacked, with each consisting of: (1) a\n                    <jats:bold>GIG vertex-level updating (GVU)<\/jats:bold>\n                    module that individually updates the graph in every GIG vertex based on its internal information; and (2) a\n                    <jats:bold>global-level GIG sample updating (GGU)<\/jats:bold>\n                    module that updates graphs in all GIG vertices based on their relationships, making the updated GIG vertices become global context-aware. This way, both internal cues within the graph contained in each GIG vertex and the relationships among GIG vertices could be utilized for down-stream tasks. Experimental results demonstrate that our GIG network generalizes well for not only various generic graph analysis tasks but also real-world multi-graph data analysis (e.g., human skeleton video-based action recognition), which achieved the new state-of-the-art results on 15 out of 16 evaluated datasets. Our code is publicly available at\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/wangjs96\/Graph-in-Graph-Neural-Network\" ext-link-type=\"uri\">https:\/\/github.com\/wangjs96\/Graph-in-Graph-Neural-Network<\/jats:ext-link>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/s11263-026-02731-4","type":"journal-article","created":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T08:02:43Z","timestamp":1772870563000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Graph in Graph Neural Network"],"prefix":"10.1007","volume":"134","author":[{"given":"Jiongshu","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiankang","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hatice","family":"Gunes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siyang","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,7]]},"reference":[{"issue":"1","key":"2731_CR1","doi-asserted-by":"publisher","first-page":"3123","DOI":"10.1038\/s41598-024-53778-7","volume":"14","author":"S Abbas","year":"2024","unstructured":"Abbas, S., Ojo, S., Al Hejaili, A., Sampedro, G. 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