The Structure and Function of Complex Networks

The Structure and Function of Complex Networks M. E. J. Newman

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The Structure and Function of Complex Networks 2003 SIAM Review / arXiv 10.1137/S003614450342480 cond-mat/0303516 newman2003-complex-networks newman2003-complex-networks.txt, the project's staged copy e7dd29ebf2f8abce31efe6baeb0016b3a910aea4 arxiv-open network-science

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them existence Quotation withheld because this record is not cleared for redistribution. structure and function of complex networks Quotation withheld because this record is not cleared for redistribution. review review Quotation withheld because this record is not cleared for redistribution. mechanisms generative network models - random graphs and growth with preferential attachment - reproduce the observed structure of real networks (skewed degree distributions, small-world, clustering) Quotation withheld because this record is not cleared for redistribution. the crucial theoretical developments in the field remain open what this limits: the theoretical claims of the review: IT REMAINS TO BE SEEN WHAT THE CRUCIAL THEORETICAL DEVELOPMENTS WILL BE IN THIS AREA Quotation withheld because this record is not cleared for redistribution. The review acknowledges that the study of networks is incomplete and that only some of the described network variants are covered by the work it reviews. what this limits: the coverage of the survey: THE STUDY OF NETWORKS IS BY NO MEANS A COMPLETE SCIENCE YET, AND MANY OF THE POSSIBILITIES HAVE YET TO BE EXPLORED IN DEPTH Quotation withheld because this record is not cleared for redistribution. The field reviewed has no systematic programme for characterising network structure, so the measures surveyed may not be the important ones. what this limits: every structural measure surveyed: WE DO NOT YET, AS WE DO IN SOME OTHER FIELDS, HAVE A SYSTEMATIC PROGRAM FOR CHARACTERIZING NETWORK STRUCTURE - the measures are ad hoc by the review's own account Quotation withheld because this record is not cleared for redistribution. Little can be reported on the third aim of the field - the effect of structure on system behaviour - because that work is only beginning. what this limits: any structure-to-behaviour claim: STUDIES OF THE EFFECTS OF STRUCTURE ON SYSTEM BEHAVIOR ... ARE STILL IN THEIR INFANCY Quotation withheld because this record is not cleared for redistribution. The review closes by stating that the whole subject it surveys is at an early stage. what this limits: the settledness of everything the review surveys: THE STUDY OF COMPLEX NETWORKS IS STILL IN ITS INFANCY Quotation withheld because this record is not cleared for redistribution. The name in general use is stated to overreach: only the degree distribution is scale-free, while other properties of the same networks do have scales. what this limits: the term scale-free network as a description of the whole network: the review states only the degree distribution is scale-free and other properties usually do have scales Quotation withheld because this record is not cleared for redistribution. Two different exponents for the same citation network were published by the same author: 2.5 to 3, then 3.04. what this limits: a published power-law exponent for a citation network: this review records the same author revising his own value in a later paper Quotation withheld because this record is not cleared for redistribution. building the study of complex networks on the foundation of mathematical graph theory, with statistical-physics methods Quotation withheld because this record is not cleared for redistribution. scale-free network scale-free network Quotation withheld because this record is not cleared for redistribution. degree distribution degree distribution Quotation withheld because this record is not cleared for redistribution. network network Quotation withheld because this record is not cleared for redistribution. clustering coefficient clustering coefficient about this quote: THE TERM IS NOT IN THE QUOTE - the quote's 'C' is the clustering coefficient, which the paper defines two paragraphs earlier ('defining a clustering coefficient C thus'). That definition is not quoted because the equation it introduces did not survive text extraction. Quotation withheld because this record is not cleared for redistribution. connectivity connectivity Quotation withheld because this record is not cleared for redistribution. assortative mixing assortative mixing Quotation withheld because this record is not cleared for redistribution. homophily homophily Quotation withheld because this record is not cleared for redistribution. fraction of transitive triples fraction of transitive triples Quotation withheld because this record is not cleared for redistribution. Vertex Vertex Quotation withheld because this record is not cleared for redistribution. Edge Edge Quotation withheld because this record is not cleared for redistribution. network transitivity network transitivity Quotation withheld because this record is not cleared for redistribution. site site Quotation withheld because this record is not cleared for redistribution. node node Quotation withheld because this record is not cleared for redistribution. actor actor Quotation withheld because this record is not cleared for redistribution. bond bond Quotation withheld because this record is not cleared for redistribution. link link Quotation withheld because this record is not cleared for redistribution. tie tie Quotation withheld because this record is not cleared for redistribution. clustering clustering Quotation withheld because this record is not cleared for redistribution. scale-free network - the term in general use, which the review says applies only to the degree distribution and not to the network's other properties Quotation withheld because this record is not cleared for redistribution. network - the stipulated vocabulary of the review: a set of items called vertices, with connections between them called edges Quotation withheld because this record is not cleared for redistribution. `connectivity` - A NAME THIS REVIEW REFUSES, AND IT SAYS WHY: `Quotation withheld` A refusal grounded in COLLISION WITH A NEIGHBOURING FIELD rather than in the term being wrong - the new usage is intelligible and is declined because the word is already taken. Quotation withheld because this record is not cleared for redistribution. `network density` - THE SAME WORDS NAMING A DIFFERENT QUANTITY BY FIELD: in sociology it names the LOCAL clustering coefficient Ci of a single vertex, which is what this passage records. Elsewhere `density` names the global edge count over possible edges. A reader who imports the sociological sense into the physics literature is reading a per-vertex quantity as a whole-graph one. Quotation withheld because this record is not cleared for redistribution. `assortative mixing` / `homophily` / `assortative matching` - ONE PHENOMENON, THREE NAMES, AND THE REVIEW ATTRIBUTES EACH TO ITS FIELD: `called assortative mixing or homophily` in social networks and epidemiology, while `the term ASSORTATIVE MATCHING is also seen in THE ECOLOGY LITERATURE, particularly in reference to mate choice among animals`. The ecological name carries a narrower referent - mate choice - inside the same concept. Quotation withheld because this record is not cleared for redistribution. `clustering coefficient` / `fraction of transitive triples` - ONE QUANTITY, TWO FIELD-LOCAL NAMES, and the review is explicit that the DEFINITION is the same one: `The definition of C given here has been widely used in the sociology literature, where it is referred to as the “fraction of transitive triples”.` FILED AS A SENSE AND NOT AS A `renamed-across-fields` EDGE ON PURPOSE: the gate requires a renaming clause to contain BOTH names, and this one calls the physics-side quantity `C` rather than `clustering coefficient`. The only span naming both runs back through Eq. (3). A CLAUSE NAMING ONE NAME IS A DEFINITION, NOT A RENAMING - the gate is right, and the reading survives at the sense layer where it is grounded in what the sentence actually says. Quotation withheld because this record is not cleared for redistribution. `Vertex` / `site` / `node` / `actor` - ONE OBJECT, FOUR NAMES, AND THE PAPER PRINTS THE DISCIPLINE BESIDE EACH. `The fundamental unit of a network, also called a site (physics), a node (computer science), or an actor (sociology).` This is the corpus's cleanest instance of renaming-across-fields: not reconstructed from two papers that never cite each other, but asserted in a glossary by an author who works in all three literatures. The same sentence does it AGAIN for `Edge` / `bond` / `link` / `tie`, with the same three fields in the same order. Quotation withheld because this record is not cleared for redistribution. `clustering` - A NAME THAT COLLIDES INSIDE ITS OWN FIELD, AND THE PAPER SAYS SO WHILE USING IT. `Quotation withheld` The other meaning is community detection. The alias is not across fields - it is a collision WITHIN one, and the author records the ambiguity rather than resolving it. Quotation withheld because this record is not cleared for redistribution. qualifies → Barabási and Albert, preferential attachment differs in: WHICH NAME THE MODEL TRAVELS UNDER, AND THE REVIEW SAYS THE EARLIER ONE DID NOT: 'The work of PRICE himself, however, is LARGELY UNKNOWN in the scientific community, and CUMULATIVE ADVANTAGE did not achieve currency as a model of network growth until its REDISCOVERY some decades later by Barabási and Albert, Quotation withheld.' One mechanism, two names, and the currency followed the second - so a search on either name finds only half the literature Quotation withheld because this record is not cleared for redistribution. contradicts → the preferential-attachment model as a model of the Web differs in: WHETHER THE MODEL'S OWN PREDICTION APPEARS IN THE DATA IT IS APPLIED TO. The model implies older vertices have higher degree; 'This correlation between degree and age has been used by Adamic and Huberman to argue against the model as a model of the World Wide Web - Quotation withheld.' The refutation is of the model AS APPLIED TO THE WEB, not of the mechanism in general Quotation withheld because this record is not cleared for redistribution. reinterprets → Milgram's small-world experiment differs in: WHAT THE SAME EXPERIMENT IS EVIDENCE FOR. 'there is another conclusion that can be drawn from this experiment which Milgram apparently failed to notice; it was pointed out in 2000 by Kleinberg' - roughly three decades later. The finding was in the data the whole time and needed a different question asked of it, which is the strongest kind of case for a layer that records what a result was taken to show Quotation withheld because this record is not cleared for redistribution. scale-free network —operationalised-as→ degree distribution scale-free network degree distribution strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says only the degree distributions of such networks are scale-free; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. assortative mixing —same-as→ homophily assortative mixing homophily the relation itself is separately evidenced · strength of the relation: 1 · note: 'called assortative mixing OR homophily' - a bare disjunction, no hedge, and the review uses both terms interchangeably thereafter. · the relation stated: the review names them as alternatives for one another in the same clause Quotation withheld because this record is not cleared for redistribution. Vertex —renamed-across-fields→ site Vertex site the relation itself is separately evidenced · strength of the relation: 1 · note: THE PAPER NAMES THE DISCIPLINE ITSELF - 'site (physics)' - so the field boundary is the paper's claim, not our inference. 'site' on its own is an ordinary English word; the discipline label is what makes this edge safe to traverse, and it lives here. · the relation stated: also called a site (physics) Quotation withheld because this record is not cleared for redistribution. Vertex —renamed-across-fields→ node Vertex node the relation itself is separately evidenced · strength of the relation: 1 · note: THE PAPER NAMES THE DISCIPLINE ITSELF - 'node (computer science)' - so the field boundary is the paper's claim, not our inference. 'node' on its own is an ordinary English word; the discipline label is what makes this edge safe to traverse, and it lives here. · the relation stated: also called a node (computer science) Quotation withheld because this record is not cleared for redistribution. Vertex —renamed-across-fields→ actor Vertex actor the relation itself is separately evidenced · strength of the relation: 1 · note: THE PAPER NAMES THE DISCIPLINE ITSELF - 'actor (sociology)' - so the field boundary is the paper's claim, not our inference. 'actor' on its own is an ordinary English word; the discipline label is what makes this edge safe to traverse, and it lives here. · the relation stated: also called a actor (sociology) Quotation withheld because this record is not cleared for redistribution. Edge —renamed-across-fields→ bond Edge bond the relation itself is separately evidenced · strength of the relation: 1 · note: THE PAPER NAMES THE DISCIPLINE ITSELF - 'bond (physics)' - so the field boundary is the paper's claim, not our inference. 'bond' on its own is an ordinary English word; the discipline label is what makes this edge safe to traverse, and it lives here. · the relation stated: also called a bond (physics) Quotation withheld because this record is not cleared for redistribution. Edge —renamed-across-fields→ link Edge link the relation itself is separately evidenced · strength of the relation: 1 · note: THE PAPER NAMES THE DISCIPLINE ITSELF - 'link (computer science)' - so the field boundary is the paper's claim, not our inference. 'link' on its own is an ordinary English word; the discipline label is what makes this edge safe to traverse, and it lives here. · the relation stated: also called a link (computer science) Quotation withheld because this record is not cleared for redistribution. Edge —renamed-across-fields→ tie Edge tie the relation itself is separately evidenced · strength of the relation: 1 · note: THE PAPER NAMES THE DISCIPLINE ITSELF - 'tie (sociology)' - so the field boundary is the paper's claim, not our inference. 'tie' on its own is an ordinary English word; the discipline label is what makes this edge safe to traverse, and it lives here. · the relation stated: also called a tie (sociology) Quotation withheld because this record is not cleared for redistribution. network transitivity —renamed-across-fields→ clustering network transitivity clustering the relation itself is separately evidenced · strength of the relation: 0.8 · note: AN ALIAS THE PAPER SUPPLIES AND SIMULTANEOUSLY WARNS AGAINST: 'although the latter…'. Weight 0.8, not 1.0 - 'sometimes also called' is itself a hedge, and the paper is recording usage it does not endorse. · the relation stated: sometimes also called clustering Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says transitivity is 'sometimes also called clustering', a term with another meaning; renamed-across-fields is loose. Quotation withheld because this record is not cleared for redistribution. A review of network science covering the small-world effect, degree distributions, clustering, network correlations, random graph models, models of growth and preferential attachment, and dynamical processes on networks. Quotation withheld because this record is not cleared for redistribution. Inspired by empirical studies of the Internet, social networks and biological networks, researchers have developed techniques and models to understand or predict the behavior of these systems. 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. network network Quotation withheld because this record is not cleared for redistribution. correlation correlation Quotation withheld because this record is not cleared for redistribution. hypothesis-testing hypothesis-testing Quotation withheld because this record is not cleared for redistribution. mean mean Quotation withheld because this record is not cleared for redistribution. sample-size sample-size Quotation withheld because this record is not cleared for redistribution. statistical-significance statistical-significance Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1137/S003614450342480.