The Anatomy of the Facebook Social Graph Johan Ugander Brian Karrer Lars Backstrom Cameron Marlow

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 The Anatomy of the Facebook Social Graph 2011 arXiv 1111.4503 ugander2011-facebook-graph ugander2011-facebook-graph.txt, the project's staged copy 67935c8e181bd9df95da456f483538fd1ba4e858 arxiv-open sociology

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 0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. network-analysis Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. what this limits: any country-level result: country assignment relies on geo-IP data, imperfect and reliable only at national granularity Quotation withheld because this record is not cleared for redistribution. what this limits: the completeness of the structural picture: WE HAVE CERTAINLY NOT EXHAUSTED THE POSSIBILITIES OF NETWORK ANALYSIS Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. active user Quotation withheld because this record is not cleared for redistribution. degrees of separation Quotation withheld because this record is not cleared for redistribution. short path lengths Quotation withheld because this record is not cleared for redistribution. local clustering coefficient Quotation withheld because this record is not cleared for redistribution. hubs Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. short path lengths degrees of separation 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. Quotation withheld because this record is not cleared for redistribution. active user hubs 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. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. assortativity Quotation withheld because this record is not cleared for redistribution. connected component Quotation withheld because this record is not cleared for redistribution. correlation Quotation withheld because this record is not cleared for redistribution. mean 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. Quotation withheld because this record is not cleared for redistribution. median 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. Quotation withheld because this record is not cleared for redistribution. sample-size Quotation withheld because this record is not cleared for redistribution. statistical-significance Quotation withheld because this record is not cleared for redistribution.

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