phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | structure of the Facebook social graph— “In this work, we characterize the structure of the world’s largest online social network, Facebook, in an effort to advance the state of the art in the empirical study of social networks.” | |
| claim-type | existence— “First, we characterize the global structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component, and we confirm the ‘six degrees of separation’ phenomenon on a global scale.” | |
| method — evidence | — “Unless otherwise noted, calculations were performed on a Hadoop cluster with 2,250 machines, using the Hadoop/Hive data analysis framework developed at Facebook [45, 46].” | |
| transfer | from the sociology of friendship networks: 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— “Feld’s observation that ‘your friends have more friends than you’ is an important psychological paradox, applying to friendship as well as sexual partners.” | transfers[0] |
| mechanism | 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— “We defined a user of Facebook as an active member of the social network if they logged into the site in the last 28 days from our time of measurement in May 2011 and had at least one Facebook friend. We note that this definition is not precisely Facebook’s ordinary definition of active user, and therefore some of our statistics differ… | mechanisms[0] |
| mechanism | 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— “Then another thread of research has measured some large-scale network properties of the Facebook graph through sampling, crawling, and other methods to collect network data [22,23]. Notably, these methodologies have no way of distinguishing between active and stale accounts. Unlike these studies, we analyze the entire Facebook graph in… | mechanisms[1] |
| mechanism | 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 diameter is an extremal measure, and it is commonly considered less interesting than the full neighborhood function, which measures what percentile of vertex pairs are within a given distance. The exact diameter can be wildly distorted by the presence of a single ill-connected path in some peripheral region of the graph, while the… | mechanisms[2] |
| mechanism | 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— “We conclude, like Ref. [23], that strict power-law models are inappropriate for Facebook’s degree distribution. It is not our intent, though, to determine which parametric form best models the distribution. The relevant results are the monotonicity and curvature of the degree distribution, the degrees of typical users, the large variance in… | mechanisms[3] |
| mechanism | 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— “The NZ algorithm, a type of Union-Find algorithm with path compression, records component structure dynamically as edges are added to a network that begins completely empty of edges. When all edges are added, the algorithm has computed the component structure of the network. Crucially for our purposes, the NZ algorithm does not require the… | mechanisms[4] |
| mechanism | 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— “For analyzing network neighborhoods, 5,000 users were randomly selected using reservoir sampling for each of 100 log-spaced neighborhood sizes, creating a sample of 500,000 users for which the analysis was performed. The percentiles shown for the clustering coefficient and degeneracy for each neighborhood size are therefore empirical… | mechanisms[5] |
| mechanism | 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— “For path length calculations, neighborhood functions were computed on a single 24-core machine with 72 GB of RAM using the HyperANF algorithm [48], averaging across 10 runs.” | mechanisms[6] |
| mechanism | 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— “Our analysis predated the existence of ‘subscriptions’ on Facebook, and in this work we study only reciprocal Facebook friendships.” | mechanisms[7] |
| replicates | the small-world / six-degrees-of-separation phenomenon (Milgram)— “the average distance between pairs of users was 4.7” | claim_relations[0] |
| replicates | Stanley Milgram's 'six degrees of separation' experiments [26]— “Short path lengths between individuals, the so-called “six degrees of separation” found by Stanley Milgram’s experiments investigating the social network of the United States [26], are here seen in Facebook on a global scale.” | claim_relations[1] |
| extends | Feld's friendship paradox ('your friends have more friends than you') [30]— “This phenomena has been discussed at length by Feld [30], and Facebook displays the effect on a grand scale.” | claim_relations[2] |
| builds-on | Watts and Strogatz's small-world networks [44]— “Many other empirical networks, social and non-social, have also been observed with these characteristics, and Watts and Strogatz called networks with these properties ‘smallworld networks’ [44].” | claim_relations[3] |
| sense | '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— “We defined a user of Facebook as an active member of the social network if they logged into the site in the last 28 days from our time of measurement in May 2011 and had at least one Facebook friend. We note that this definition is not precisely Facebook’s ordinary definition of active user, and therefore some of our statistics differ… | senses[0] |
| sense | '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 | senses[1] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[2] |
| control | the entire Facebook graph analysed in anonymised form rather than a sample, restricted to active accounts reliably corresponding to people — held — rules out 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[0] |
| control | the structural results compared against those from smaller social networks — partial — rules out 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[1] |
| note | short path lengths —same-as→ degrees of separation — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[0] |
| audit | active user —contrasted-with→ hubs — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[1] |
| outcome (stated by the tagger, no quotation) | control — held | controls[0] |
| outcome (stated by the tagger, no quotation) | control — partial | controls[1] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| for which use | limitation — any country-level result: country assignment relies on geo-IP data, imperfect and reliable only at national granularity Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| for which use | limitation — the completeness of the structural picture: WE HAVE CERTAINLY NOT EXHAUSTED THE POSSIBILITIES OF NETWORK ANALYSIS Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| replication | untested | |
| limitation | The paper's own definition of an 'active' user departs from Facebook's, so its statistics differ from company figures. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| limitation | Country assignment relies on geo-IP data, which is imperfect and only reliable at national granularity. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| limitation | The analysis is acknowledged as non-exhaustive with respect to available network measures. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| limitation | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| limitation | The object studied is an abstraction the authors themselves call limited. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| limitation | A small group of accounts sits far outside the typical user, so the average describes nobody in particular. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | The Facebook graph is nearly fully connected (99.91% of individuals in one large component), the six-degrees phenomenon is confirmed on a global scale, and the average distance in May 2011 was 4.7. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[0] |
| not machine-vouched | finding — 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. | content_tags.findings[0] |
| finding | The Facebook graph as a whole is clearly sparse, yet users' neighborhoods contain surprisingly dense structure. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[1] |
| quantity | 721 million active users — size of the Facebook graph analysed (May 2011) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[0] |
| quantity | 99.91% — fraction of users in the single large connected component Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[1] |
| quantity | 4.7 hops — average distance between Facebook users (May 2011) — four degrees Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[2] |
| definition | assortativity Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[0] |
| definition | connected component Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[1] |
| key-terms | graph, users, network, clustering, degree, friendships, assortativity, neighborhoods, social |
| concept | active user Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[5] |
| concept | degrees of separation Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[6] |
| concept | short path lengths Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[7] |
| concept | local clustering coefficient Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[8] |
| concept | hubs Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[9] |
| correlation r | as written: r = 0.226 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[0] |
| mean μ | as written: mean of Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
| evidence status note | mean — 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. | content_tags.statistics[1] |
| median | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[2] |
| evidence status note | median — 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. | content_tags.statistics[2] |
| sample-size n/N | as written: n = 721 million Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[3] |
| statistical-significance | as written: significantly Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[4] |
When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.
Tag layer © the Meta-Tagging Project, CC BY 4.0. The paper text is © its authors/publisher
and is linked, not reproduced. Excerpts shown are short quotations for identification and verification.
· back to index
· concepts · authors
· עברית
© 2026 Shir Sivroni · ORCID 0009-0000-2597-2824