{"as_of":"2026-08-08T06:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:62c185427ce860c66b25fdbdff3237f4996659a7884692b7833cde4e827da766","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:50:05.391632Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.07026/citation-record","integrity":"/paper/2506.07026/integrity","json":"/paper/2506.07026/citation-record.json","paper":"/paper/2506.07026"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.764209Z","title":"Error and attack tolerance of complex networks","venue":null,"work_id":"c90a67f7-338b-4b30-82dd-7d98080d580c","year":2000},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.272670Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:1a98a7e08783fec01c3d631eb093d70a0d6180c60d1ac3380aba060882004e6b","observation_id":"0c6651bd-1b4c-416a-a27f-096b0da3a0b9","resolution":{"observed_at":"2026-08-07T05:50:05.767247Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.755513Z","title":"A framework for second-order eigenvector centralities and clustering coefficients","venue":null,"work_id":"7ecc4505-8a92-48e4-9ad2-fd6b8bf22450","year":2020},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.276156Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:7c3806d06af49bf098872918e55aab151788f647c362812820aab2caf5cc81a6","observation_id":"511116a7-50a9-4fb6-bb37-d1cfa2765df1","resolution":{"observed_at":"2026-08-07T05:50:05.758611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.747348Z","title":"Betweenness centrality in large complex networks","venue":null,"work_id":"2c111aff-ee68-4532-8559-b4d9f722da2a","year":2004},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.279158Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:823510c1839d95eb425033b5347d487e48276bcdb1e035ba13f25cff8df57985","observation_id":"17674f24-5a19-4958-8b16-d50955c02be9","resolution":{"observed_at":"2026-08-07T05:50:05.750327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.737763Z","title":"Three hypergraph eigenvector centralities","venue":null,"work_id":"dc41d0b2-8289-4348-b24d-06048a6fd09f","year":2019},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.282079Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:bd7f79138220fad0fe988c15e5d28dbc1b48712c081a6b5a90b2c0ad1d7d5764","observation_id":"79816466-e4d4-47d9-802a-dbf13044966b","resolution":{"observed_at":"2026-08-07T05:50:05.741368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.729675Z","title":"A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks","venue":null,"work_id":"ebc26201-e725-4fa0-b9f4-b3c5adbd48b5","year":2018},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.285053Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:4b3e8742c48d2e94b95347be6046cab34cdf66bb50f3d73aaba0b80fe7cc7f69","observation_id":"af4c90b7-0362-4adf-ad30-9d115f7f7752","resolution":{"observed_at":"2026-08-07T05:50:05.732632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.721784Z","title":"Factoring and weighting approaches to status scores and clique identification","venue":null,"work_id":"ea83f457-3edb-411d-bf7e-a7f17af820f7","year":1972},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.288446Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:903d14a8f9991c60ef7f155e4d7bcd51a1115a30e3b5527ca32566abe9933571","observation_id":"6f910c26-7b79-436a-b6e6-8a117b4f4d1e","resolution":{"observed_at":"2026-08-07T05:50:05.724788Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.713100Z","title":"A family of centrality measures for graph data based on subgraphs","venue":null,"work_id":"c75703f1-3380-4f9f-834b-4460f000b4b1","year":2024},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.291609Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:6ad4e281617133240a0c9ffd09dff6a6657ce2eab10cef19ae27b94230a71c2e","observation_id":"13bb5e0b-46cb-49d6-9d48-f4b9040daade","resolution":{"observed_at":"2026-08-07T05:50:05.716491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.703903Z","title":"Triangle centrality","venue":null,"work_id":"658dd4e7-bb9d-4bc2-8606-5329afba2616","year":2024},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.294519Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:3b2d93c0723a31dc1c6345878e8665f6e6434e191b28e89b3e9d44adb3d05e42","observation_id":"70f17c36-1f43-4012-a338-22e1b2a620cd","resolution":{"observed_at":"2026-08-07T05:50:05.707699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.694495Z","title":"Perron-frobenius theorem for nonnegative tensors","venue":null,"work_id":"b1f4b0ba-eddd-42d6-8fe5-256924ab756a","year":2008},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.297891Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:7ad24de4f05c84b7596878d65043efa6d5526add121e43c51b38c3d455b70892","observation_id":"8a3f83b1-1178-48b9-ba89-125a5a5c68ef","resolution":{"observed_at":"2026-08-07T05:50:05.698081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.685802Z","title":"Higher-order link prediction using triangle embeddings","venue":null,"work_id":"90cc49bd-c71a-44d7-8b8b-1a2e1087122d","year":2020},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.300539Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:9f6ac6d817654ea49f312b219cbcaaff01569afbcf15d2066fbf2664518ea8a5","observation_id":"b00de376-9d4c-4803-960e-d88a1c38e9b8","resolution":{"observed_at":"2026-08-07T05:50:05.688935Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.676740Z","title":"Spectra of power hy- pergraphs and signed graphs via parity-closed walks","venue":null,"work_id":"f3402284-d79a-4d56-afe2-ae51c4ca21da","year":2024},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.303451Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:1b5c5e824323651ef63c5db046a9298cf47b4dddfafa37a554f909448d7b1901","observation_id":"5a01fdeb-e9fa-412f-a670-bb1e8183b96d","resolution":{"observed_at":"2026-08-07T05:50:05.680328Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.668258Z","title":"Local fiedler vector centrality for detection of deep and overlapping communities in networks","venue":null,"work_id":"024f5c34-9123-42eb-b35c-397c5b632754","year":2014},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.306633Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:8160a418e607c64cb1877079ef329464f52c4af932952c59a23e1d6bac18c567","observation_id":"7f8bfb9d-8642-4b0f-85e0-a0e01c1a25c4","resolution":{"observed_at":"2026-08-07T05:50:05.671432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.660022Z","title":"Deep community detection","venue":null,"work_id":"9f217f67-f129-4b0c-9106-08f49bb23668","year":2015},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.309454Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:b5753589b3405a1decc1a119747f167088c9b9f89f6036c92d7edb44422615c8","observation_id":"8c3a3ba9-8856-4044-81d0-90885cfca756","resolution":{"observed_at":"2026-08-07T05:50:05.662901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.650896Z","title":"Spectra of uniform hypergraphs","venue":null,"work_id":"e60eddf9-57d5-4019-acb6-e71035eb3a55","year":2012},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.312770Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:fdb18ef5db8f57fd745b2bc1a8117898c0ea6014bd22d9afcb2edc0f6270ce39","observation_id":"98006e86-e86b-41e6-b7d7-1b30f8f85e2d","resolution":{"observed_at":"2026-08-07T05:50:05.654157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.641381Z","title":"Study on centrality mea- sures in social networks: a survey","venue":null,"work_id":"efda0a5b-07d1-47cd-a3ba-068dfe18f813","year":2018},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.315627Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:9ba1675eda8e6981c0907a58bc203e3c5e8efce3d142119cac38f92fe6422f9d","observation_id":"62e01f0c-21d6-4db7-997d-1250e0ca1407","resolution":{"observed_at":"2026-08-07T05:50:05.645213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.632724Z","title":"Communication in complex networks","venue":null,"work_id":"af09b1d9-9fac-47b3-85a5-76370f4119cd","year":2022},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.318306Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:8da405d5a44fb9986de8de1aae74c407eb6fb05ab7d6ca3352e80c6455fa932a","observation_id":"eda045f2-621b-46ca-a00d-7ca4233d0cc2","resolution":{"observed_at":"2026-08-07T05:50:05.635807Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.624565Z","title":"Degree relations of triangles in real-world networks and graph models","venue":null,"work_id":"393aceb4-a364-45cd-8c6b-c3d715365f44","year":2012},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.320823Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:025debc742d661f462eca232161cb57973614a7316a932c89b5629ea491dca2c","observation_id":"0c516e48-4958-4020-a834-ee9f07c930b0","resolution":{"observed_at":"2026-08-07T05:50:05.627703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.616028Z","title":"Perron communica- bility and sensitivity of multilayer networks","venue":null,"work_id":"b2f0cf4d-fedf-41f1-ada9-873280b758c5","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.324140Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:788899458e3e9409dd9220f872b6f9ef17c27ca322745f3b2f06ecf57bc5d13e","observation_id":"e6973b11-1665-4d9b-ae2c-3aeb8cf76713","resolution":{"observed_at":"2026-08-07T05:50:05.619170Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.608288Z","title":"Subgraph centrality in com- plex networks","venue":null,"work_id":"f72becbc-185c-4971-9a87-ef7a6894c4fc","year":2005},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.326974Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:0624d8d06e019336532317595bbc550a4fa85fbaac3c481ccdf6e58260e8d8bb","observation_id":"24c5d0d4-f529-4f22-b8ee-1a672dff1fbc","resolution":{"observed_at":"2026-08-07T05:50:05.611057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.599610Z","title":"A property of eigenvectors of nonnegative symmetric matri- ces and its application to graph theory","venue":null,"work_id":"4116d689-4be7-4aaa-b6e9-b6259aeb31b2","year":1975},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.330049Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:2e74e92745397a66c44000b8a8d3d27e1b852e1936f97cef1f2ea34ab432b00a","observation_id":"12585266-f667-4b87-b51c-a0610448863c","resolution":{"observed_at":"2026-08-07T05:50:05.602829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.590504Z","title":"Centrality in valued graphs: A measure of betweenness based on network flow","venue":null,"work_id":"c3b11004-93ba-4a32-ab0b-61736b4e71dc","year":1991},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.333000Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:0ec65b2a81307d490d2730f9864c2249b59a2cafdbd03d7e82e12792ae6edfc3","observation_id":"203bc0d5-8fab-4bc3-98ee-39b3a902d4ba","resolution":{"observed_at":"2026-08-07T05:50:05.593836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.581870Z","title":"Perron–frobenius theo- rem for nonnegative multilinear forms and extensions","venue":null,"work_id":"8c6e01a4-d428-4c00-9856-c9351ab4f74f","year":2013},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.336017Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:c90e6a5eb3ba74af13e281f4d1569d61ab89926750301ba4e04c36e62d7556b0","observation_id":"e407ba27-8d5a-4911-8ae6-b28b933e6da0","resolution":{"observed_at":"2026-08-07T05:50:05.585092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.573421Z","title":"Graph clustering using triangle- aware measures in large networks","venue":null,"work_id":"fe103f6d-4730-487f-b6e6-40c79d2aa275","year":2022},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.338770Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:32c581fb1bed291a6f2e3cfc2253181c563a24885353a80cc9e43810d527dd2d","observation_id":"b5805b48-6b2a-46f1-a11d-ca2241792172","resolution":{"observed_at":"2026-08-07T05:50:05.576684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.565517Z","title":"Triangular stability maximization by influence spread over social networks","venue":null,"work_id":"693e23a5-340a-439c-b3a0-b5109b15414f","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.342049Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:77f40f34c9b1f38d8b2edd4e84713fbe34b41ac7a51f3b072fff1c7c5fe1ae04","observation_id":"217970a4-2ce6-4013-8027-0d2699aa8d27","resolution":{"observed_at":"2026-08-07T05:50:05.568530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.556992Z","title":"Searching for key cycles in a complex network","venue":null,"work_id":"7c4fa340-5451-467d-9104-99ecda2fd2aa","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.345159Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:d139f557792b704c46ac72607123a154fc4408edb0890737273e8ad924bea8d7","observation_id":"0ad1c553-322b-4414-a88c-fc9b5ab1b248","resolution":{"observed_at":"2026-08-07T05:50:05.560402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.549315Z","title":"A new measure of centrality for brain networks","venue":null,"work_id":"bca27845-c450-4040-806e-e19c6d0d58cd","year":2010},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.347965Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:95ee7b7a90a49dfa0fde62ce49789853286e720438800c18b3a57e0ae2a7bce0","observation_id":"ad400e02-4f06-485b-b0ef-e0e9d35fd5e5","resolution":{"observed_at":"2026-08-07T05:50:05.552147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.540902Z","title":"A critical review of centrality measures in social networks","venue":null,"work_id":"81b91067-5335-4fe4-8c0e-31415d7076b1","year":2010},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.351130Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:0dd304d8a944c285bee3615eefc30afa64a389b1dc10679305e51d44c1d653b7","observation_id":"be06f6fd-19ef-41b8-9850-f14376793ac3","resolution":{"observed_at":"2026-08-07T05:50:05.543941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.532296Z","title":"Singular values and eigenvalues of tensors: a variational ap- proach","venue":null,"work_id":"a64b5e86-ad11-4b9a-8f3c-0ab04fd9df9a","year":2005},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.353805Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:79e28706e8db6f27962690ec5d4f4da302026e84f704b5e2c7b87ede32a25251","observation_id":"8f803e6a-7698-4272-9425-5461ee67a8c6","resolution":{"observed_at":"2026-08-07T05:50:05.535314Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.523356Z","title":"On a generalization of the spectral mantel’s theorem","venue":null,"work_id":"cc8236bb-ce42-4d86-9c30-6a2070caf7c5","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.357030Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:bce870299a4b9b60881b4a1aded4d3c2259739106e76f97ceffe1c5587cbb834","observation_id":"2db494a9-b65e-41f4-84e5-8d90af723662","resolution":{"observed_at":"2026-08-07T05:50:05.526942Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.515358Z","title":"The high order spectrum of a graph and its applications in graph colouring and clique counting","venue":null,"work_id":"80d04bc7-e85e-417a-91b6-49f61c6de202","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.359781Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:61a4e4fbc6b1e9b5b52b31d3e5cf456633cae293dfafeca86e8b6eedba2db1e7","observation_id":"7af53545-68d1-4c3b-ab98-4337cde8e571","resolution":{"observed_at":"2026-08-07T05:50:05.518329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.507007Z","title":"Eigenvector centrality mapping for analyzing con- nectivity patterns in fMRI Data of the human brain","venue":null,"work_id":"f6ab6f72-34e2-4e51-b8d1-c6c5b1513b48","year":2010},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.362742Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:71361f11f42fe54b51e8a523eda7e6d6701fa73b7561dbcd57f54005444e6957","observation_id":"fb4c3f29-8923-408e-a8ae-04a53f1894ef","resolution":{"observed_at":"2026-08-07T05:50:05.509962Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.497217Z","title":null,"venue":null,"work_id":"de8a98fb-be1d-4ea5-a499-93bd974b349e","year":2003},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.365553Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:fc2af67ac0e69cde6aed6e183f417ea3718a78c40b7673fb2bb7b551de9208aa","observation_id":"cd2f9106-5101-4de2-9dbb-c572c2f401a6","resolution":{"observed_at":"2026-08-07T05:50:05.500881Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.487426Z","title":"The local triangle structure centrality method to rank nodes in networks","venue":null,"work_id":"c4649849-2744-4949-a6ed-cd729aa3ef83","year":2019},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.368649Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:54d2c119386732ad2f6f3b601d6282468a97984fa5d10899edb01617901a2d75","observation_id":"faa023e7-6887-4eb6-ae94-4ddd23d97879","resolution":{"observed_at":"2026-08-07T05:50:05.491015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.478664Z","title":"Eigenvalues of a real supersymmetric tensor","venue":null,"work_id":"ddeb9481-ffa0-4d86-86c4-f6b7ce2ca700","year":2005},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.371388Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:3d0018543c48b38f146fa00ac047c8e2821f1bfeaefb36acb7de0aabd6084466","observation_id":"cf47f937-d2b9-4195-a6d5-7b9eb5de3e4d","resolution":{"observed_at":"2026-08-07T05:50:05.481761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.469736Z","title":"Tensor Analysis: Spectral Theory and Special Tensors","venue":null,"work_id":"f4ea017c-433e-48ec-9fd6-d55d7f89bd31","year":2017},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.374241Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:8f77ab133bdb68af7ef64780e9145e25e86706523d910690f0cceb371f1346cc","observation_id":"2ead4393-cc0e-4231-bcbc-d0f17c0bb63e","resolution":{"observed_at":"2026-08-07T05:50:05.472896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.460176Z","title":"The network data repository with interactive graph analytics and visualization","venue":null,"work_id":"26ac5502-c34b-4f6d-a7cd-f5058abb042f","year":2015},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.376928Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:83d8a81b70c59bf5256c6101806d6217daa99d035765a1d7a22dbd1c52d7e7dc","observation_id":"0cb5cddc-9fc3-461c-9acd-9f58029b9ced","resolution":{"observed_at":"2026-08-07T05:50:05.463605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.450206Z","title":"Node and edge nonlinear eigenvec- tor centrality for hypergraphs","venue":null,"work_id":"74504f26-d578-4cba-a5e9-de4962c4455a","year":2021},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.380367Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:3e8078b81e95484e93debdb9314cfa4bbcd4e91e83e594ae73fb66c1844a9030","observation_id":"5fe298bc-5205-48ca-922d-b5b4e547a69a","resolution":{"observed_at":"2026-08-07T05:50:05.453581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.440812Z","title":"The two-steps eigenvector centrality in complex networks","venue":null,"work_id":"984ee68e-3972-43ce-90f0-224d2a5df67d","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.383312Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:d7596ad78f0c19803b63d072526788cfee933828783efa9f0a07806f288510d5","observation_id":"63907607-8796-4fc7-bdfe-7cf20bf00d65","resolution":{"observed_at":"2026-08-07T05:50:05.444009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.431747Z","title":"An information flow model for conflict and fission in small groups","venue":null,"work_id":"212e0dda-9766-43e9-8cc9-8a0ea975615a","year":1977},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.386159Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:48d9d5d2b0dbbfbbc8961de4840459250fa23a1015586df77db5b9ef809f6329","observation_id":"26641b53-f0fe-4b83-9ce7-6c119b352e63","resolution":{"observed_at":"2026-08-07T05:50:05.434826Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.422865Z","title":"Community detection via a tri- angle and edge combination conductance partitioning","venue":null,"work_id":"b3c14c24-6da2-4fe0-b308-fa67e7d4127c","year":2020},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.388801Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:15a1f3487d60a0b03be82a7a7a0662bb8af8b2fda0a13229989cf39cedf5341e","observation_id":"27634112-293f-4a28-9bf9-eeaca3e7ac2d","resolution":{"observed_at":"2026-08-07T05:50:05.425970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:50:05.411059Z","title":"Estrada index and subgraph cen- trality of hypergraphs via tensors","venue":null,"work_id":"6a047a56-fa94-42f8-ba91-593ba0aeb2e1","year":2023},"citing_paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T05:50:05.391632Z"},"links":{"citing_paper":"/paper/2506.07026"},"observation_digest":"sha256:0550aa27c5372ef341d827ffcf83849920d0710ca5c4e546d9fc2943addf248f","observation_id":"70391312-c923-4c22-bc2d-5a1dba9686e3","resolution":{"observed_at":"2026-08-07T05:50:05.416768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.07026","last_updated":"2025-06-08T07:28:24Z","latest_version":1,"primary_category":"cs.SI","snapshot_observed_at":"2026-08-07T05:41:23.163746Z","submitted_at":"2025-06-08T07:28:24Z","title":"An $\\alpha$-triangle eigenvector centrality of graphs"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":40},"total_outbound_references":41},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2506.07026."}