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Here we systematically investigate how does the graph structure of neural networks affect their predictive performance. To this end, we develop a novel graph-based representation of neural networks called relational graph, where layers of neural network computation correspond to rounds of message exchange along the graph structure. Using this representation we show that: (1) a \"sweet spot\" of relational graphs leads to neural networks with significantly improved predictive performance; (2) neural network's performance is approximately a smooth function of the clustering coefficient and average path length of its relational graph; (3) our findings are consistent across many different tasks and datasets; (4) the sweet spot can be identified efficiently; (5) top-performing neural networks have graph structure surprisingly similar to those of real biological neural networks. Our work opens new directions for the design of neural architectures and the understanding on neural networks in general.","url_abs":"https://arxiv.org/abs/2007.06559v2","url_pdf":"https://arxiv.org/pdf/2007.06559v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"graph-structure-of-neural-networks","repo_url":"https://github.com/facebookresearch/graph2nn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"graph-structure-of-neural-networks","repo_url":"https://github.com/CuriousCat-7/Graph-Structure-of-Neural-Networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"graph-structure-of-neural-networks","repo_url":"https://github.com/Waasem/RobDanns","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"CC0-1.0"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2007.06559","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2007.06559"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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