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Paper Citation Record · LEDGER

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs

As of 12 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2508.21506.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.21506 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T14:27:44.164776Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

  • verified exact4
  • verified fuzzy12
  • unresolved13
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 305a90de-ac0b-4a55-89bf-716467dc0189 · outbound

This paper cites Ahmad, M.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Ahmad, M

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:48.976034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:41.726902Z digest=sha256:d7edeea6d4bc51f021b9c1493921766c8e0e9d7d77f30e1b54a0f8ce3c0b495d

Observation 694be528-178f-4cc5-a154-9318034add70 · outbound

This paper cites On the Edge Derivative of the Normalized Laplacian with Applications to Kemeny's Constant.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs On the Edge Derivative of the Normalized Laplacian with Applications to Kemeny's Constant

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-05T14:27:44.766366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:41.797534Z digest=sha256:1b0c11646c5d9905f4d13f17a1f688530f45e758d0a4309e045529fb952e7299

Observation fd252772-2ac8-4e0e-8281-6431064c93ec · outbound

This paper cites Altafini, D.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Altafini, D

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:48.821344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:41.904139Z digest=sha256:5fc923d11bde95a539fae1420070235d846e8813920175500487da5833416743

Observation bec5e92e-bd11-48e9-b045-694ec5f1cbce · outbound

This paper cites Benzi and P.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Benzi and P

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:48.673666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:41.985578Z digest=sha256:d7d4698983143f697d6ca24a90f2196b95331639dd7d30d11937d2945efee3ef

Observation 469fae23-5836-4066-8764-85f328884c56 · outbound

This paper cites Changing the ranking in eigenvector centrality of a weighted graph by small perturbations.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Changing the ranking in eigenvector centrality of a weighted graph by small perturbations

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-05T14:27:44.625878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.063255Z digest=sha256:20ad7160b6344af45ceb92bb74b6f9795674f3251ae0f837930a34a155dcd621

Observation 97d3632a-6447-4c55-b46a-2b8130e71ac7 · outbound

This paper cites Benzi and C.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Benzi and C

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:48.509810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.147829Z digest=sha256:1ca78b55b8a744a443875a43d3d65086b5010478a9f1f34287b4b5870c56658f

Observation be94ffad-a236-43b1-80cd-5bdda7cab56b · outbound

This paper cites Berkhout and B.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Berkhout and B

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:48.353493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.252358Z digest=sha256:73a973a84686975edd9725111e12d6b77cd5086d7e94125c4bae60d5322fdaad

Observation ab3f7a66-ff1d-4f05-b759-268fd48ab2c4 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:48.170439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.355492Z digest=sha256:1523130464a98b87b80d774bd902cef418c0aa11492eafd48919dd529464b5fd

Observation 2cb55229-96c1-4970-9cda-147275716482 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:48.016156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.451029Z digest=sha256:fc38ddfdf67b4f4762319b778667664fa31a5609e28954849be50cd666d74fae

Observation a73c11ab-cd0b-46dc-967c-6c3651b9e62f · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:47.809199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.528534Z digest=sha256:3ecf93306914f9dae68a81a0f1cec6cd011fa49268d2c79eb157b77af2df23b5

Observation db3e6e91-09d9-4ae3-b11d-9d6ced30155a · outbound

This paper cites Breen and S.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Breen and S

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:47.625399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.616126Z digest=sha256:ea78d22a88a1a8cd425b176ff5898204444229bb4bb12fb117e7278f1ce4a71b

Observation 5cc83786-f6af-4e5f-9e1c-6a2d8953938a · outbound

This paper cites Cipolla, F.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Cipolla, F

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:47.476452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.715837Z digest=sha256:a599276d2af6ccbc8e3843c38569bcd0886fd36af9309eb71e989f7b9c66ea69

Observation a7418a59-1061-40ef-85e4-aa2077f11b61 · outbound

This paper cites Crisostomi, S.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Crisostomi, S

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:47.341780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.797852Z digest=sha256:410e39bc05d808546e5ce18800e94f206e7f807a51d52c3447aae55274562f70

Observation d2bc4b66-c573-4633-b021-1d0b4172117b · outbound

This paper cites Cuthill and J.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Cuthill and J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:47.157247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:42.897395Z digest=sha256:4df2c52407834bbe968005cb97126a5cf03e8d1e8d482e850189dbdc69b414df

Observation 5e874cb9-4d05-4965-aa65-b4b315fbd249 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:47.013628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.002537Z digest=sha256:65139a2b0f874c60e4761b163f9f4230fe2c9bac2374030ff8f6e8df08fad3d0

Observation f3345bab-4184-46bb-9a2d-cead03141b18 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:46.809485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.104283Z digest=sha256:b09906c238c7d444ff779ea4483d836487b3f5da0b97c065835c2bda50458e35

Observation b415f4a3-c6ab-4996-86cd-18f9a8eb704e · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:46.545334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.214748Z digest=sha256:b51d45064d86f88cf572faa9cc9db3b948aaccbf0bc749ce2be6e32e11d3cd60

Observation bff83e76-f1ab-49de-8941-93a7328e46fa · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:46.475099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.310887Z digest=sha256:3a54130d1a866bc951cb472e1699d49a9ed6c80accd295b7d8ec662e32684534

Observation 57146f20-1fff-40d0-96d9-508211e13576 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:46.344381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.390217Z digest=sha256:2b8ee6a1275583526d066713fc7943770fb7e876ec8bd2ee2e990e451c5f8fda

Observation d1ff8996-10c5-4776-b4a0-e528e9fbff1b · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:46.181790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.446406Z digest=sha256:b30f8c72a2775b99b3489260d895fe09b4ab6fbba9db04d2b7a3b525377067c8

Observation 93ba1434-4097-4a56-a6fc-82bb5ea4d972 · outbound

This paper cites Kemeny and J.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Kemeny and J

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:45.990234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.547988Z digest=sha256:8dbac6a9599e53ec2283fc382a363b85937d2a1f9ecc018bfa7ea81feaac2e4e

Observation fb8991a7-0902-4cb0-9c73-3183412b9cf7 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:45.793104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.639546Z digest=sha256:45a06edec43eacea78fe33340d3e87bd58b1f97db5f75b2f0f1879975ff54d0c

Observation 43a84b37-6d6f-48de-b282-e27ad0266897 · outbound

This paper cites Edge Addition and the Change in Kemeny's Constant.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Edge Addition and the Change in Kemeny's Constant

Reference 23

Resolution
verified exact
local_arxiv, observed 2026-08-05T14:27:44.470537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.713978Z digest=sha256:181fcb8677507498b6a83c64425ee8de9c123d155567b97f5dbf2666fa5b868c

Observation 14e6813a-fcd1-4a3b-815b-3a2832e85235 · outbound

This paper cites Liben-Nowell and J.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Liben-Nowell and J

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:45.591136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.778170Z digest=sha256:23a1b68b9d5ea8b0a66c5179c82deffdb02eaec0ff83e6e2c3b2610fdc84b1da

Observation c050b856-7bfb-441e-8ac8-985ff4c3fe87 · outbound

This paper cites Finding community structure in networks using the eigenvectors of matrices.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Finding community structure in networks using the eigenvectors of matrices

Reference 25

Resolution
verified exact
local_arxiv, observed 2026-08-05T14:27:44.329354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.842923Z digest=sha256:280ea935e55f53df7a8519a06a9d8bf032fd53289753862fcff1467f57e37c80

Observation e97712e6-6210-4b05-9798-7f51f2d994e2 · outbound

This paper cites Patel, P.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Patel, P

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T14:27:45.412552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.918604Z digest=sha256:b5c74b985a34df70e2011bbecd1c0bf81a0faa530a373ac4f70abdcfb17eac23

Observation 9c31a04f-9414-403a-b39a-92c0013c9b76 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:45.276581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:43.985757Z digest=sha256:4db808a1494c8eaf505035ee8d9fd908eaa517c6d30a973b3707e4f535c7474d

Observation fc651aeb-9fb8-4ecc-8558-eee6782378cf · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:45.091981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:44.063540Z digest=sha256:759a8097600b41c512002dbe3bb67087ba5814a308cf1be51e54c8a106287b11

Observation efcf2b1e-cb4f-4520-9ec3-096817a815d4 · outbound

This paper cites an unresolved cited work.

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-05T14:27:44.925401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T14:27:44.164776Z digest=sha256:fbc2c6f10ad9ea4474ba95ed7b3d44ff0b12fdd487a56a79d8796566aae5563a

Pith citing papers

No inbound Pith citation observations are available.