Paper Citation Record · LEDGER

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2506.02686.

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

pith.paper-citation-record.v1
2506.02686 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:28:33.971198Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

31 of 31 outbound references displayed

verified exact4
verified fuzzy20
unresolved4
parse uncertain0
malformed identifier3
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7b46f1b1-7330-46cb-9777-df2671d8df98 · outbound

This paper cites Detecting the ultra low dimensionality of real networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Detecting the ultra low dimensionality of real networks

Reference 1

Resolution: verified exact; doi, observed 2026-08-07T11:28:34.443176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 23c517b0-addb-44ae-a4d6-3a0d28738f5c · outbound

This paper cites Community detection in complex networks using randomisation.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Community detection in complex networks using randomisation

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:38.987502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0be27a75-29a2-4794-8781-c33c7041a0f7 · outbound

This paper cites Emergence of scaling in random networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Emergence of scaling in random networks

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:38.812323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3ac5279b-9115-40fe-b8cd-e67add81b9e5 · outbound

This paper cites Sus- taining the Internet with hyperbolic mapping.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Sus- taining the Internet with hyperbolic mapping

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:38.613759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 83477cbf-96fe-4a10-bc8d-79104ab73397 · outbound

This paper cites Small worlds and clustering in spatial networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Small worlds and clustering in spatial networks

Reference 5

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Source-reported events for the cited work

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Observation 90fc8346-c8f4-4992-bb5d-310b5e06f0b3 · outbound

This paper cites Community Detection in the Hyperbolic Space.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Community Detection in the Hyperbolic Space

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:28:34.922039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b0963eb2-f5c3-4624-90a6-3b83bf88bf4c · outbound

This paper cites Random hyperbolic graphs ind+ 1 dimensions.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Random hyperbolic graphs ind+ 1 dimensions

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T11:28:32.063242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fddba30d-d129-4f57-a286-e3fa0d2677d0 · outbound

This paper cites Epidemics in a synthetic urban population with multiple levels of mixing.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Epidemics in a synthetic urban population with multiple levels of mixing

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:38.357026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0f14bfdb-cc06-4a10-9af3-e2276246f369 · outbound

This paper cites On community structure in complex networks: chal- lenges and opportunities.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures On community structure in complex networks: chal- lenges and opportunities

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:38.124392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f5011c53-b00b-4927-9feb-3c5d08e5eaa3 · outbound

This paper cites All scale-free networks are sparse.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures All scale-free networks are sparse

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:37.908368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 94439db2-de91-4762-8a99-de636208a2cb · outbound

This paper cites Dimension mat- ters when modeling network communities in hyperbolic spaces.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Dimension mat- ters when modeling network communities in hyperbolic spaces

Reference 11

Resolution: malformed identifier; no resolver link, observed 2026-08-07T11:28:32.353484Z

Source-reported events for the cited work

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Observation 2524179b-e064-4afe-a45f-0c2614e39c0a · outbound

This paper cites Characterizing the Anal- ogy Between Hyperbolic Embedding and Community Structure of Com- plex Networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Characterizing the Anal- ogy Between Hyperbolic Embedding and Community Structure of Com- plex Networks

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:37.660837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6728228b-9ea8-4f40-8b38-2c363e4ade32 · outbound

This paper cites Soft communities in similarity space.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Soft communities in similarity space

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:37.449299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 316bedd8-c069-4a1d-a78d-e4b6837f59f5 · outbound

This paper cites Community structure in social and biological networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Community structure in social and biological networks

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:37.199628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cbef5ccf-7b36-4e82-9d4b-23442da0e94e · outbound

This paper cites The Hidden- Degree Geometric Block Model.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures The Hidden- Degree Geometric Block Model

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:36.957240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5b4d5c77-574b-4c72-8b39-acc7691b765c · outbound

This paper cites The D-Mercator method for the multidimen- sional hyperbolic embedding of real networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures The D-Mercator method for the multidimen- sional hyperbolic embedding of real networks

Reference 16

Resolution: malformed identifier; no resolver link, observed 2026-08-07T11:28:32.668067Z

Source-reported events for the cited work

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Observation 5e27c6c1-b95c-486f-9f26-d26af465ad78 · outbound

This paper cites Generalised popularity- similarity optimisation model for growing hyperbolic networks beyond two dimensions.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Generalised popularity- similarity optimisation model for growing hyperbolic networks beyond two dimensions

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:36.782735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a9f89296-cfcd-4ee8-b283-4cd32ae9df60 · outbound

This paper cites The inherent community structure of hyperbolic networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures The inherent community structure of hyperbolic networks

Reference 18

Resolution: verified exact; doi, observed 2026-08-07T11:28:34.214447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7e57ff4d-33cd-41bc-bf07-90d01e52b2f2 · outbound

This paper cites Clustering Implies Geometry in Networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Clustering Implies Geometry in Networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T11:28:32.887646Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24ad1e58-d778-4be1-9897-7081839f09c9 · outbound

This paper cites Hyperbolic geometry of complex networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Hyperbolic geometry of complex networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T11:28:32.966095Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73ea1654-9339-45e0-89e1-3bd2c16c1827 · outbound

This paper cites A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:36.568464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 772f312d-4fb8-42ca-a504-13c38780bc85 · outbound

This paper cites Angular separability of data clusters or network communities in geometrical space and its relevance to hyperbolic embedding.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Angular separability of data clusters or network communities in geometrical space and its relevance to hyperbolic embedding

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:28:34.733437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 933192f9-bf99-4158-ba3b-3c3b62cbd9c7 · outbound

This paper cites Popularity versus similarity in growing networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Popularity versus similarity in growing networks

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:36.343595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8240b763-67f1-4f6c-92aa-edafc74c0186 · outbound

This paper cites Dynamics and control of diseases in networks with community structure.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Dynamics and control of diseases in networks with community structure

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:36.174464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f3e81611-35e7-46b9-8485-7348d38ad5ce · outbound

This paper cites The Shortest Path to Network Geometry: A Practical Guide to Basic Models and Applications, Elements in Structure and Dynamics of Complex Networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures The Shortest Path to Network Geometry: A Practical Guide to Basic Models and Applications, Elements in Structure and Dynamics of Complex Networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:35.939948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7f6fc654-2a44-4c68-8040-0bd54805da94 · outbound

This paper cites A model for social networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures A model for social networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:35.773634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2786c1c7-da1b-406d-b3c5-fec1948cfd50 · outbound

This paper cites Hyperbolic mapping of complex networks based on community information.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Hyperbolic mapping of complex networks based on community information

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:35.586511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5e35f20e-402d-4ea9-8da4-632c1e5f1f4b · outbound

This paper cites Collective dynamics of ‘small- world’networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Collective dynamics of ‘small- world’networks

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:35.394538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cbaceb2b-d65c-4059-8310-617e62951800 · outbound

This paper cites High dimensional hyperbolic geometry of complex networks.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures High dimensional hyperbolic geometry of complex networks

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:35.284418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ab3860f8-b735-4237-ad79-1667ea54fc23 · outbound

This paper cites Community preserving mapping for network hyper- bolic embedding.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Community preserving mapping for network hyper- bolic embedding

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T11:28:33.888244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9379b0b2-b56f-4949-9759-0fd468cf81ed · outbound

This paper cites Emergence of soft communities from geometric preferential attachment.

Random Hyperbolic Graphs with Arbitrary Mesoscale Structures Emergence of soft communities from geometric preferential attachment

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:28:35.110274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.