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In this paper, we define a weighted skew adjacency matrix with Rand\\'c weight, the skew Randi\\'c matrix ${\\bf R_S}(G^\\sigma)$, of $G^\\sigma$ as the real skew symmetric matrix $[(r_s)_{ij}]$ where $(r_s)_{ij} = (d_id_j)^{-\\frac{1}{2}}$ and $(r_s)_{ji} = -(d_id_j)^{-\\frac{1}{2}}$ if $v_i \\rightarrow v_j$ is an arc of $G^\\sigma$, otherwise $(r_s)_{ij} = (r_s)_{ji} = 0$. We derive some pr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.1300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-05T09:02:35Z","cross_cats_sorted":[],"title_canon_sha256":"7b2d26b5c0a1790a210529e222c0d58daa637fe009ba17385e5f3387a115d291","abstract_canon_sha256":"0c8e31499df3277dda43714989150d3b4f9815b6eb8720c28d5210d68fa1f5eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:31.959463Z","signature_b64":"EnQYnJ8nmFLSugwsAPnY7zIZzNFhbt43h0SgmvXxh/Y98pDbP/c7Sef7fYk/8ZV+JXQEctvgnUyQv2Pb7G30DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4f5e0f0a2278e7bf0746a6c9841b8383ba718c3c655c3c2a4b23973eba86eb3","last_reissued_at":"2026-05-18T02:30:31.958831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:31.958831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew Randi\\'c Matrix and Skew Randi\\'c Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fei Huang, Ran Gu, Xueliang Li","submitted_at":"2014-06-05T09:02:35Z","abstract_excerpt":"Let $G$ be a simple graph with an orientation $\\sigma$, which assigns to each edge a direction so that $G^\\sigma$ becomes a directed graph. $G$ is said to be the underlying graph of the directed graph $G^\\sigma$. In this paper, we define a weighted skew adjacency matrix with Rand\\'c weight, the skew Randi\\'c matrix ${\\bf R_S}(G^\\sigma)$, of $G^\\sigma$ as the real skew symmetric matrix $[(r_s)_{ij}]$ where $(r_s)_{ij} = (d_id_j)^{-\\frac{1}{2}}$ and $(r_s)_{ji} = -(d_id_j)^{-\\frac{1}{2}}$ if $v_i \\rightarrow v_j$ is an arc of $G^\\sigma$, otherwise $(r_s)_{ij} = (r_s)_{ji} = 0$. 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