The Anatomy of the Facebook Social Graph

Johan Ugander, Brian Karrer, Lars Backstrom, Cameron Marlow · arXiv · 2011 · sociology · record ugander2011-facebook-graph
tag layer · index · concepts · authors · עברית

Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. Replication_status set to 'replicated' because the paper frames its central claims as confirmations of previously established phenomena (Milgram's six degrees, Feld's friendship paradox, Watts–Strogatz small-world properties) at global scale; it simultaneously disagrees with power-law degree-distribution claims ("strict power-law models are inappropriate for Facebook’s degree distribution"), so the agreement is partial — the abstract itself says the comparison finds "mostly, but not entirely, agreement". The disagreement with Ref. [23]/[24,25] on power laws was not recorded as a claim_relation because those works are cited only by number, not named. 2026-08-14, 2026-08-16 and 2026-08-25 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node. Update, 15 September 2026: EXCEPTION, measured with the merge gate's own predicate (Paper.locate): 1 quote(s) on this record are not found as one exact string in the current staged text - content_tags.findings[0].evidence. The sentence above does not hold for them as written. Where a row records why - the quote is grounded in another copy of the paper, joins two passages with an ellipsis, or differs from the staged text by extraction noise - that note stays on the row. Update, 16 September 2026: EXCEPTION TO THE DATED PASS ABOVE, on this record only: this record carries 1 composite quote field - a quote assembled from two or more passages joined by an ellipsis. A COMPOSITE IS NOT AN EXACT CONTIGUOUS SUBSTRING of the staged text and is deliberately not anchored: each of its parts is verified separately at the offsets in evidence composite spans, and a part occurring more than once carries span null rather than a guessed offset. So the 'every quote verified as an exact substring' clause of the dated pass above DOES NOT HOLD for those fields, and never did - the parts were verified, the whole was not. Nothing is deleted, re-grounded or withdrawn: this writes down an exception that was always true of composites and had not been recorded, so a reader was told more than the pass had checked.

The quality of the text these quotes were cut from. symbol-font-not-extractable: 4 '(cid:NNN)' glyph-index markers remain in a staged text of 44,247 characters, where the PDF's embedded font had no ToUnicode map. THE QUOTES ON THIS RECORD ARE THE PAPER'S AND THE STAGED COPY IS THE DAMAGED ONE - which is the opposite of the usual case and is why it went unnoticed: one of its 52 live quotes is not an exact substring of this text, and it could NOT be located in it even by aligning the quote's WORD SEQUENCE under this damage, so the defect recorded here is present on the record but does not by itself account for the miss. Not repaired in place: editing the staged text moves every offset after the edit and re-hashes every anchor on the record. Measured at 113aae60fefc3eb1, re-measured unchanged at 54b63482778ddf56.

1 quote on this page was cut from a different copy of this article. This project holds two extractions of this paper: the plain text every other quote here is anchored in, and the publisher’s own HTML edition, which we are not licensed to republish. It is verbatim in the second and cannot be found in the first — not because the tagging is wrong, but because the extraction damaged the passage: a page number dropped into the middle of a number, a formula moved out of its sentence, a ligature where two letters belong. The record names the copy for each one. The quote is the paper’s; the extraction is not.

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Other fields define these differently the same word, defined another way in another discipline
sample-size 5 fields · clustering 3 fields · graph 2 fields · statistical-significance 2 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 10 concept tags on this paper, 5 are grounded in a quoted sentence.

social network degree distribution clustering coefficient small-world effect assortativity active user degrees of separation short path lengths local clustering coefficient hubs the population is fixed by a STIPULATED definition of an active user - logged in within the last 28 days AND holding at least one friend - and the authors state that this is not the platform's own definition and that their statistics therefore differ from company figures the whole graph is analysed rather than sampled or crawled, and the stated reason is a defect of the alternatives rather than a preference: sampling and crawling cannot tell an active account from a stale one the neighbourhood function is used in place of the diameter, because the diameter is an extremal measure that a single ill-connected path in a peripheral region can wildly distort, while a percentile of vertex pairs is robust to it the paper rejects the power-law model for its degree distribution and then DECLINES to fit a replacement, naming instead the features of the distribution it takes to be the relevant results the component structure is computed by a union-find algorithm with path compression that records components as edges are added, which is chosen because IT DOES NOT REQUIRE THE EDGES TO BE HELD IN MEMORY - the whole edge list is streamed past a single machine instead neighbourhood statistics are estimated from a stratified sample rather than the whole graph: users are drawn by reservoir sampling at each of a hundred log-spaced neighbourhood sizes, and the reported percentiles are stated to be empirical percentiles of that sample rather than of the population the path-length figures are produced by running the neighbourhood-function algorithm repeatedly on one machine and AVERAGING ACROSS THE RUNS rather than computing once the edge relation is restricted to RECIPROCAL friendships only, and the authors date the restriction: the analysis predated the existence of subscriptions on the platform graph users network clustering degree friendships neighborhoods social connected component correlation mean mean of median sample-size statistical-significance network-analysis

Method, as described: large-scale-network-analysis

Legend

relation to other work	`claim_relations`	how this paper stands to another: agrees, contradicts, extends, qualifies
claim type	`claim_type`	the shape of the claim: existence, mechanism, method, critique, prediction, null
concept edge	`concept_edges`	an asserted relation between two concepts, with the sentence asserting it
concept	`concepts`	an idea the paper works with, quoted where the paper uses it
content tag	`content_tags`	a finding, definition, quantity, statistic or variable named in the paper
control	`controls`	an experiment run to eliminate a rival explanation
limitation	`limitations`	what the paper says its evidence cannot support
mechanism	`mechanisms`	how the reported effect is said to come about
method	`method`	how the paper produced its evidence
phenomenon	`phenomenon`	the effect or regularity under study
sense	`senses`	a distinct use of a term, quoted where the paper fixes it
transfer	`transfers`	a method or concept carried in from another field

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://arxiv.org/abs/1111.4503. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 4 · claim_type 1 · concept_edges 2 · concepts 5 · content_tags 11 · controls 2 · limitations 6 · mechanisms 8 · method 1 · phenomenon 1 · senses 3 · transfers 1

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 2 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facet	tag	field	conf.	whose words
claim_type	existence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_type`		the paper's words
phenomenon	structure of the Facebook social graph Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`phenomenon`		the paper's words
method	network-analysis Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: network-analysis	`method`		the paper's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the population is fixed by a STIPULATED definition of an active user - logged in within the last 28 days AND holding at least one friend - and the authors state that this is not the platform's own definition and that their statistics therefore differ from company figures	`mechanisms[0]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the whole graph is analysed rather than sampled or crawled, and the stated reason is a defect of the alternatives rather than a preference: sampling and crawling cannot tell an active account from a stale one	`mechanisms[1]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the neighbourhood function is used in place of the diameter, because the diameter is an extremal measure that a single ill-connected path in a peripheral region can wildly distort, while a percentile of vertex pairs is robust to it	`mechanisms[2]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the paper rejects the power-law model for its degree distribution and then DECLINES to fit a replacement, naming instead the features of the distribution it takes to be the relevant results	`mechanisms[3]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the component structure is computed by a union-find algorithm with path compression that records components as edges are added, which is chosen because IT DOES NOT REQUIRE THE EDGES TO BE HELD IN MEMORY - the whole edge list is streamed past a single machine instead	`mechanisms[4]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: neighbourhood statistics are estimated from a stratified sample rather than the whole graph: users are drawn by reservoir sampling at each of a hundred log-spaced neighbourhood sizes, and the reported percentiles are stated to be empirical percentiles of that sample rather than of the population	`mechanisms[5]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the path-length figures are produced by running the neighbourhood-function algorithm repeatedly on one machine and AVERAGING ACROSS THE RUNS rather than computing once	`mechanisms[6]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the edge relation is restricted to RECIPROCAL friendships only, and the authors date the restriction: the analysis predated the existence of subscriptions on the platform	`mechanisms[7]`	0.85	the tagger's words
limitations	The paper's own definition of an 'active' user departs from Facebook's, so its statistics differ from company figures. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: every comparison between this paper's statistics and Facebook's: THIS DEFINITION IS NOT PRECISELY FACEBOOK'S ORDINARY DEFINITION OF ACTIVE USER, AND THEREFORE SOME OF OUR STATISTICS DIFFER SLIGHTLY FROM COMPANY STATISTICS	`limitations[0]`		the tagger's words
limitations	Country assignment relies on geo-IP data, which is imperfect and only reliable at national granularity. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any country-level result: country assignment relies on geo-IP data, imperfect and reliable only at national granularity	`limitations[1]`		the tagger's words
limitations	The analysis is acknowledged as non-exhaustive with respect to available network measures. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the completeness of the structural picture: WE HAVE CERTAINLY NOT EXHAUSTED THE POSSIBILITIES OF NETWORK ANALYSIS	`limitations[2]`		the tagger's words
limitations	The 'six degrees' confirmation is a statement about percentages of pairs in a friendship graph, not a repeat of the experiment that produced the phrase. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the claim that this work confirms six degrees of separation: what is reported is that 92% of all pairs of Facebook users were within five degrees and 99.6% within six, measured as shortest paths in the friendship graph	`limitations[3]`	1.0	the tagger's words
limitations	The object studied is an abstraction the authors themselves call limited. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any social conclusion drawn from this graph: the authors describe the network abstraction of human relationships as certainly limited, while useful for characterising social relationships	`limitations[4]`	1.0	the tagger's words
limitations	A small group of accounts sits far outside the typical user, so the average describes nobody in particular. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: an average degree quoted from this paper: a small population of users with abnormally high degrees, called hubs in the networks literature, have degrees far larger than the average or median user	`limitations[5]`	1.0	the tagger's words
transfers	Feld's friendship paradox - that your friends have more friends than you do - taken as the frame for reading the degree distribution of the whole Facebook graph Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`transfers[0]`	0.85	the tagger's words
controls	the entire Facebook graph analysed in anonymised form rather than a sample, restricted to active accounts reliably corresponding to people Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: sampling bias, which the paper names as the standing problem of online social network research - there is no sample to be unrepresentative of the whole when the whole is the data · outcome (stated by the tagger, no quotation): held	`controls[0]`	0.85	the tagger's words
controls	the structural results compared against those from smaller social networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: a structural property that belongs to Facebook's scale or design rather than to social networks - and the comparison is reported as agreeing only in part · outcome (stated by the tagger, no quotation): partial	`controls[1]`	0.85	the tagger's words
concepts	active user Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: active user	`concepts[5]`		the paper's words
concepts	degrees of separation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: degrees of separation	`concepts[6]`		the paper's words
concepts	short path lengths Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: short path lengths	`concepts[7]`		the paper's words
concepts	local clustering coefficient Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: local clustering coefficient	`concepts[8]`		the paper's words
concepts	hubs Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: hubs	`concepts[9]`		the paper's words
senses	'active user' - STIPULATED, AND EXPLICITLY NOT THE PLATFORM'S: logged in within 28 days and holding at least one friend, which the authors state is not Facebook's ordinary definition and is why their statistics differ from the company's; the 721 million figure counts exactly what this sentence picks out Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[0]`	1.0	the tagger's words
senses	'six degrees of separation' - MILGRAM'S PHRASE ON A DIFFERENT INSTRUMENT: the original is letter-forwarding chains among Americans, this is shortest paths in a friendship graph, and the paper says the phenomenon is here SEEN in Facebook rather than claiming the two measurements are the same Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[1]`	1.0	the tagger's words
senses	the local clustering coefficient - READ AS A PERCENTAGE OF FRIEND PAIRS: an average coefficient of 0.14 for users with 100 friends is glossed as 14% of a median user's friend pairs being friends themselves, so an average over users is reported as a fact about a median one Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[2]`	1.0	the tagger's words
claim_relations	replicates → the small-world / six-degrees-of-separation phenomenon (Milgram) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[0]`		the tagger's words
claim_relations	replicates → Stanley Milgram's 'six degrees of separation' experiments [26] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[1]`		the tagger's words
claim_relations	extends → Feld's friendship paradox ('your friends have more friends than you') [30] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[2]`		the tagger's words
claim_relations	builds-on → Watts and Strogatz's small-world networks [44] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[3]`		the tagger's words
concept_edges	short path lengths —same-as→ degrees of separation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: 2026-08-15: READ THIS EDGE WITH senses[1]: the sense on this record that quotes the SAME SENTENCE says these are two different measurements: 'Milgram's phrase on a different instrument - the original is letter-forwarding chains among Americans, this is shortest paths in a friendship graph'. A path length in a friendship graph and a chain of acquaintances who forwarded a letter are not the same quantity. The type is left as it stands pending the wider decision about what 'same-as' asserts; this note exists so the two are read together. also in: short path lengths · degrees of separation	`concept_edges[0]`		the tagger's words
concept_edges	active user —contrasted-with→ hubs Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span describes hubs as users with abnormally high degree; it does not contrast them with active users. also in: active user · hubs	`concept_edges[1]`		the tagger's words
content_tags	721 million — size of the Facebook graph analysed (May 2011) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[0]`		the tagger's words
content_tags	99.91% — fraction of users in the single large connected component Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[1]`		the tagger's words
content_tags	4.7 — average distance between Facebook users (May 2011) — four degrees Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[2]`		the tagger's words
content_tags	The Facebook graph as a whole is clearly sparse, yet users' neighborhoods contain surprisingly dense structure. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[1]`		the tagger's words
content_tags	assortativity Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: assortativity	`content_tags.definitions[0]`		the tagger's words
content_tags	connected component Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: connected component	`content_tags.definitions[1]`		the tagger's words
content_tags	correlation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: correlation	`content_tags.statistics[0]`		the tagger's words
content_tags	mean Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. also in: mean	`content_tags.statistics[1]`		the tagger's words
content_tags	median Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. also in: median	`content_tags.statistics[2]`		the tagger's words
content_tags	sample-size Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: sample-size	`content_tags.statistics[3]`		the tagger's words
content_tags	statistical-significance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: statistical-significance	`content_tags.statistics[4]`		the tagger's words

Interpretive choices

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content_tags.findings[0] — quotation withheld — the page has already reproduced as much of this paper as the rights budget allows
NOT MACHINE-VOUCHED: declared-ellipsis - An elided quote: its 2 pieces ('the social network is nearly fully conne' ... 'en users on Facebook in May 2011 was 4.7') are each in our copy of the paper, and the quote marks the cut with an ellipsis, so the joined string is in no copy. Located mechanically, piece by piece.

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