Epidemic Spreading in Scale-Free Networks

Romualdo Pastor-Satorras, Alessandro Vespignani · Physical Review Letters / arXiv · 2001 · epidemiology · 10.1103/PhysRevLett.86.3200 · record pastorsatorras2001-epidemic-scalefree
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. limitations left empty: the paper states no limits on its own results; the nearest thing is a claim of robustness (finite-size effects excluded, generalisable to 2 < gamma <= 3), which is the opposite of a limitation. Only one claim_relation recorded: the paper takes its scale-free graph from 'the algorithm devised in Refs. [6]' and its data from 'the Virus Bulletin [16]', but these targets appear as bare reference numbers with no author or work named in the running text, so per the rules they were not turned into relations. Method is really twofold (large-scale simulation plus a mean-field analytic solution); the facet records the simulation. The extraction garbles all mathematics (e.g. 'hk2i', 'ki/ Pj kj') and splices page numbers into the middle of sentences ('Quotation withheld'), so quotes were taken only from unbroken prose stretches. 2026-08-12 and 2026-08-15 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, 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 Nothing is deleted, re-grounded or withdrawn: this writes down an exception that was always true of composites and had not been recorded, so a reader was told more than the pass had checked. 2026-09-16 the project CORRECTION TO THE EXEMPTION ABOVE, SAME DAY: THE EXEMPTION DOES NOT APPLY TO THIS RECORD. Its evidence composite spans row(s) are FOSSILS of a 2026-08-25 composite marking that was superseded by a 2026-08-26 re-slice; the quote is an exact contiguous substring of the staged text, so the dated substring claim above holds for it WITHOUT exception. The clause is left in place with this correction beside it rather than removed, so that the error and its repair are both on the record.

1 quote on this page may have lost a superscript, a subscript or a fraction slash. Nothing in it is corrupt — every character survived. What did not survive is POSITION: whether a digit sat above the line, below it, or between two others. So x 10 9 may be x 10⁹, chi 2 5 may be chi-squared with five degrees of freedom, and 1 2 may be one half. Read any expression here against the published paper before relying on it.

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.

How to read this page. The article itself is not reproduced here — this paper is not cleared for redistribution, so what follows is the tag layer alone. The evidence sentences are withheld with the article. The table at the foot lists every tag the record carries; each row names the facet it belongs to, and the whose words column says whether the tag records the paper's own wording or the tagger's sentence about the paper. Every tag links to each other paper in the corpus carrying it. The machine-readable edition of the same thing is the TEI file beside this one, where the tags live in standOff, and the article is at its publisher via the link below. 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.

Other fields define these differently the same word, defined another way in another discipline
threshold 2 fields · connectivity 2 fields · simulation 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 16 concept tags on this paper, 12 are grounded in a quoted sentence. 11 carry the tagger's gloss of what the term means in this paper, which is not something the article can license.

scale-free network epidemic threshold contact network degree distribution basic reproduction number scale-free networks node individual link susceptible-infected-susceptible contact process Euclidean lattice random networks Internet surviving probability prevalence the scale-free network diverging connectivity fluctuations remove the epidemic threshold, so infections persist for any positive transmission rate diverging connectivity fluctuations act as an infinite connectivity, and the threshold falls to zero a link is more likely to land on a highly connected node, so hubs are infected first and keep re-infecting the rest e-mail attachments make the contact graph the Internet's topology rather than physical proximity epidemic network scale-free spreading threshold virus power-law infection connectivity computer viruses mean-field model world-wide-web epidemic threshold λc effective spreading rate λ spreading rate λ virus prevalence statistical-significance statistically significant mean exponential-distribution simulation

Legend

second reading	`alternatives`	an independent re-reading of a facet, recorded whether or not it agrees
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
contribution	`contribution`	what the paper claims to add
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
object of study	`object_of_study`	what the paper is about — the thing it investigates
phenomenon	`phenomenon`	the effect or regularity under study
research question	`research_question`	the question the paper sets itself
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
unrecordable relation	`unhoused_relations`	a relation the paper asserts that this vocabulary cannot express, with the reason

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://doi.org/10.1103/PhysRevLett.86.3200. The reading view exists for the papers whose licence permits it.

Every tag on this page

alternatives 3 · claim_relations 6 · claim_type 1 · concept_edges 3 · concepts 12 · content_tags 25 · contribution 1 · controls 1 · limitations 4 · mechanisms 4 · method 1 · object_of_study 1 · phenomenon 1 · research_question 1 · senses 3 · transfers 2 · unhoused_relations 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 3 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facet	tag	field	conf.	whose words
object_of_study	The spread of computer viruses on the Internet, treated as an epidemic process running on a scale-free network. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`object_of_study`		the paper's words
research_question	Why do computer viruses persist for years at very low prevalence, when standard epidemic models say an infection either dies out exponentially or takes off? Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`research_question`		the paper's words
contribution	Shows that on a scale-free network the epidemic threshold vanishes, so an infection persists at any spreading rate - which explains the observed long-lived, low-prevalence computer viruses without tuning anything. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`contribution`		the paper's words
claim_type	mechanism 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	epidemic spreading on scale-free networks 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	simulation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: simulation	`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 scale-free network diverging connectivity fluctuations remove the epidemic threshold, so infections persist for any positive transmission rate	`mechanisms[0]`		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: diverging connectivity fluctuations act as an infinite connectivity, and the threshold falls to zero	`mechanisms[1]`	1.0	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: a link is more likely to land on a highly connected node, so hubs are infected first and keep re-infecting the rest	`mechanisms[2]`	0.9	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: e-mail attachments make the contact graph the Internet's topology rather than physical proximity	`mechanisms[3]`	0.9	the tagger's words
limitations	the SIS model reduces individuals to two discrete states (healthy/infected) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: every result of the SIS model: INDIVIDUALS EXIST ONLY IN TWO DISCRETE STATES	`limitations[0]`		the tagger's words
limitations	The model is run at one exponent, γ = 3, and the generalisation to other exponents is asserted qualitatively rather than shown. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the range of exponents the conclusion covers: THE PRESENT FRAMEWORK CAN BE GENERALIZED TO NETWORKS WITH 2 < gamma <= 3, RECOVERING QUALITATIVELY THE SAME RESULTS - asserted qualitatively, by citation	`limitations[1]`	0.9	the tagger's words
limitations	Individuals are reduced to two states, healthy or infected, which the paper flags as a coarse description. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the same scope as limitations[0], in the paper's own words: THIS MODEL RELIES ON A COARSE GRAINED DESCRIPTION OF INDIVIDUALS IN THE POPULATION	`limitations[2]`	1.0	the tagger's words
limitations	The empirical half rests on one industry data source over a four-year window. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the empirical half only: WE HAVE ANALYZED THE PREVALENCE DATA REPORTED BY THE VIRUS BULLETIN FROM FEBRUARY 1996 TO MARCH 2000 - one industry source, four years	`limitations[3]`	0.8	the tagger's words
transfers	modelling epidemic spreading on scale-free contact networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`transfers[0]`		the tagger's words
transfers	the susceptible-infected-susceptible model and the notion of an epidemic threshold, applied to computer virus outbreaks on the Internet Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`transfers[1]`	1.0	the tagger's words
controls	testing the model's prediction against independent real-world prevalence data reported by the Virus Bulletin, February 1996 to March 2000 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: that the absence of an epidemic threshold is an artefact of the scale-free model rather than a property of how real computer viruses spread · outcome: held	`controls[0]`	0.85	the tagger's words
concepts	epidemic threshold Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: epidemic threshold	`concepts[1]`		the paper's words
concepts	scale-free networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: scale-free networks	`concepts[5]`	1.0	the paper's words
concepts	node Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: node	`concepts[6]`	1.0	the paper's words
concepts	individual Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: individual	`concepts[7]`	1.0	the paper's words
concepts	link Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: link	`concepts[8]`	1.0	the paper's words
concepts	susceptible-infected-susceptible Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: susceptible-infected-susceptible	`concepts[9]`	1.0	the paper's words
concepts	contact process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: contact process	`concepts[10]`	1.0	the paper's words
concepts	Euclidean lattice Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Euclidean lattice	`concepts[11]`	1.0	the paper's words
concepts	random networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: random networks	`concepts[12]`	1.0	the paper's words
concepts	Internet Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Internet	`concepts[13]`	1.0	the paper's words
concepts	surviving probability Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: surviving probability	`concepts[14]`	1.0	the paper's words
concepts	prevalence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: prevalence	`concepts[15]`	1.0	the paper's words
unhoused_relations	Euclidean lattice → epidemic threshold Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. A NONZERO EPIDEMIC THRESHOLD IS A PROPERTY OF THE LOCAL-CONNECTIVITY REGIME, NOT SOMETHING THE LATTICE PRODUCES. The lattice does not increase, reduce or eliminate a threshold; models with local connectivity simply HAVE one, and that is the standard result this paper is written against. None of the eight types says 'X holds in regime Y', and none of the four effect directions says a quantity EXISTS - all four describe a change in it.	`unhoused_relations[0]`	0.95	the tagger's words
senses	network - social, biological and communication systems alike, whose nodes are individuals or organizations and whose links are the interactions among them 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	network - the Internet as the contact graph along which an e-mail-borne infection actually travels, as opposed to physical proximity 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	epidemic - a computer virus outbreak, analysed with the models of biological epidemiology 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
alternatives	claim_type: mechanism Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. a second reading reaching the same value. Recorded: mechanism — note: a second reading reaching the same value from a different sentence. Not applied - a person decides.	`alternatives.claim_type`		the tagger's words
alternatives	method: simulation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. a second reading reaching the same value. Recorded: simulation — note: a second reading reaching the same value from a different sentence. Not applied - a person decides.	`alternatives.method`		the tagger's words
alternatives	phenomenon: absence of an epidemic threshold for spreading on scale-free networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. a second reading DIFFERING from the recorded value. Recorded: epidemic spreading on scale-free networks — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides.	`alternatives.phenomenon`		the tagger's words
claim_relations	builds-on → scale-free network model 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	contradicts → the classical nonzero-epidemic-threshold prediction 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	contradicts → the standard nonzero epidemic threshold of mathematical epidemiology [11] 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 → the scale-free graph model of Barabasi and Albert [6] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[3]`	1.0	the tagger's words
claim_relations	contradicts → standard epidemic modelling on lattices and mean-field models, which predicts a nonzero threshold Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: THE AXIS IS THE CONNECTIVITY REGIME. 'Quotation withheld.' The threshold is not wrong for the models it was derived in - it is a property OF THOSE MODELS' CONNECTIVITY, and this paper changes the connectivity. Its unhoused_relations[0] in this corpus records the same point as a relation the vocabulary could not express: a threshold is a property of a regime, not something a lattice produces.	`claim_relations[4]`	1.0	the tagger's words
claim_relations	extends → the observational literature on computer virus prevalence [10,13] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[5]`	1.0	the tagger's words
concept_edges	scale-free networks —contrasted-with→ random networks 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 full span and kept, but endpoint by anaphora: 'That' = the scale-free connectivity of the Internet (previous sentence). also in: scale-free networks · random networks	`concept_edges[2]`		the tagger's words
concept_edges	contact process —is-a→ susceptible-infected-susceptible Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 0.9 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says the SIS model is a GENERALIZATION of the CP model; is-a is loose, endpoints abbreviated. also in: contact process · susceptible-infected-susceptible	`concept_edges[3]`		the tagger's words
concept_edges	EVIDENCE CORRECTED (RE-GROUNDED) · scale-free networks —causes→ epidemic threshold Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. EVIDENCE CORRECTED: RE-GROUNDED. The old span - 'annulling thus the threshold' - states the mechanism and names neither endpoint. This sentence names both AND states the finding, and the sign travels with it. — direction on the measure: eliminates · strength of the relation: 1 also in: scale-free networks · epidemic threshold	`concept_edges[4]`		the tagger's words
content_tags	γ between 2 and 3 — power-law degree exponent of the scale-free networks (Internet/WWW) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[0]`	0.85	the tagger's words
content_tags	0 (no threshold) — the epidemic threshold vanishes for scale-free networks 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	τ ≃ 14 months — characteristic lifetime of boot and macro virus strains Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[2]`	1.0	the tagger's words
content_tags	λc = 0 — the epidemic threshold on a scale-free network Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[3]`	1.0	the tagger's words
content_tags	N = 103 to N = 8.5 × 106 — range of simulated network sizes (the exponents are lost in extraction; the paper means 10^3 to 8.5x10^6) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: FLATTENED EXPONENT IN THIS QUOTE - THE NUMBER IS WRONG BY ORDERS OF MAGNITUDE AS IT STANDS. The staged text reads '8.5 × 106', where the paper writes 10 to the power 6. The superscript was pushed onto the line by the PDF extractor. The quote is verbatim to the staged text and its anchor is sound; the STAGED TEXT is what is damaged. NOT repaired - repair means re-staging the body and re-anchoring the record.	`content_tags.quantities[4]`	0.9	the tagger's words
content_tags	γ ≃ 2.5 — measured scale-free exponent of the Internet and the world-wide-web Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[5]`	1.0	the tagger's words
content_tags	100 starting configurations x 10 network realisations — averaging used for every prevalence figure Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[6]`	1.0	the tagger's words
content_tags	an epidemic threshold and its associated critical behavior are absent Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[0]`		the tagger's words
content_tags	Real computer-virus data are analysed to give the average lifetime and prevalence of viral strains on the Internet. 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	On a scale-free network the epidemic threshold is zero: any spreading rate, however small, lets the infection persist. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[2]`	1.0	the tagger's words
content_tags	Steady-state virus prevalence decays with decreasing spreading rate as ρ ~ exp(−C/λ). Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[3]`	1.0	the tagger's words
content_tags	Fitting the data gives a lifetime of about 14 months for boot and macro viruses and 6-9 months for file viruses. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[4]`	1.0	the tagger's words
content_tags	The higher a node's connectivity, the higher its probability of being infected. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[5]`	1.0	the tagger's words
content_tags	spreading rate λ Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: spreading rate λ	`content_tags.variables[0]`		the tagger's words
content_tags	effective spreading rate λ Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: effective spreading rate λ	`content_tags.variables[2]`	1.0	the tagger's words
content_tags	virus prevalence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: virus prevalence	`content_tags.variables[3]`	1.0	the tagger's words
content_tags	epidemic threshold λc Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: epidemic threshold λc	`content_tags.definitions[0]`		the tagger's words
content_tags	scale-free network Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: scale-free network	`content_tags.definitions[1]`		the tagger's words
content_tags	susceptible-infected-susceptible Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: susceptible-infected-susceptible	`content_tags.definitions[2]`	1.0	the tagger's words
content_tags	effective spreading rate λ Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: effective spreading rate λ	`content_tags.definitions[3]`	1.0	the tagger's words
content_tags	epidemic threshold Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: epidemic threshold	`content_tags.definitions[4]`	1.0	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[0]`		the tagger's words
content_tags	power-law Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: power-law	`content_tags.statistics[1]`	1.0	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. also in: mean	`content_tags.statistics[2]`	0.9	the tagger's words
content_tags	exponential-distribution Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: exponential-distribution	`content_tags.statistics[3]`	1.0	the tagger's words

Interpretive choices

Tags that could not be placed in the text:

none — every tag was located in the text

What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.