# graph

## Definitions

• WordNet 3.6
• v graph represent by means of a graph "chart the data"
• v graph plot upon a graph
• n graph a visual representation of the relations between certain quantities plotted with reference to a set of axes
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Webster's Revised Unabridged Dictionary
• Interesting fact: Coral (pro osteon) has molecular architecture and chemistry similar to human bone and so it can be used to replace bone grafts, helping bones heal faster. 150-200 pounds of it can sustain hundreds of graphs
• Graph A curve or surface, the locus of a point whose coördinates are the variables in the equation of the locus; as, a graph of the exponential function.
• Graph A diagram symbolizing a system of interrelations of variable quantities using points represented by spots, or by lines to represent the relations of continuous variables. More than one set of interrelations may be presented on one graph, in which case the spots or lines are typically distinguishable from each other, as by color, shape, thickness, continuity, etc. A diagram in which relationships between variables are represented by other visual means is sometimes called a graph, as in a bar graph, but may also be called a chart.
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Century Dictionary and Cyclopedia
• n graph A diagrammatic representation of a system of connections by means of a number of spots, which may be all distinguished from one another, some pairs of these spots being connected by lines all of which are of one kind. In this way any system of relationship may be represented. Graphs are commonly used in chemistry, and have been applied in algebra and in logic.
• n graph A terminal element in compounds of Greek origin, denoting that which writes, marks, or describes something, as in chronograph, telegraph, seismograph, etc., or, passively, that which is written, as in autograph, electrograph, etc. In the passive use the stricter form is -grammar
• n graph A curve as representing an equation or function.
• n graph A line drawn through a series of points whose position has been already determined.
• n graph A representation by points on or in a lattice.
• n graph The point of a link-motion which describes any curve.
• graph To draw a curve representing (a given equation or function).
• graph To trace graphs.
• n graph Any apparatus for duplicating drawings or writings by printing from a gelatinous surface.
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Chambers's Twentieth Century Dictionary
• n Graph graf a representation by means of lines, exhibiting the nature of the law according to which some phenomena vary: -graph is used as a terminal in many Greek compounds to denote an agent which writes, &c., as telegraph, seismograph, or the thing written, as in autograph, &c
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## Quotations

• William S. Burroughs “There is the pleasurable orgasm, like a rising sales graph, and there is the unpleasurable orgasm, slumping ominously like the Dow Jones in 1929.”
• Marshall Mcluhan “When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”

## Etymology

Webster's Revised Unabridged Dictionary
See -graph
Chambers's Twentieth Century Dictionary
Gr. graphē, a writing—graphein, to write.

## Usage

### In literature:

I doubt if he really thinks of human beings as human beings; on the contrary, some engineering graph represents humanity in his mind.
"The Mirrors of Washington" by Anonymous
Then a graph can be plotted to show the improvement from day to day.
"The Science of Human Nature" by William Henry Pyle
He went through the Kinsey books and absorbed a lot of data and graphs and figures on human behavior that meant nothing to him.
"The Fourth R" by George Oliver Smith
With such a machine, we can run off a graph of the tides for years ahead.
"The Sky Is Falling" by Lester del Rey
But that 'graph was never made.
"Brigands of the Moon" by Ray Cummings
We shall have navigated the rings of Saturn, and perhaps graphed them from his surface.
"A Honeymoon in Space" by George Griffith
At Wellesley, the graph in Fig.
"Applied Eugenics" by Paul Popenoe and Roswell Hill Johnson
It will be noted that the middle section of the graph represents the "mental ages" falling between 15 and 17.
"The Measurement of Intelligence" by Lewis Madison Terman
He can be marked, measured and entered on a graph.
"The K-Factor" by Harry Harrison (AKA Henry Maxwell Dempsey)
Most of them were graphs of functions of light, considered as a wave in these experiments.
"The Ultimate Weapon" by John Wood Campbell
But she suddenly raised her hand and pointed to the radar-graph instrument.
"The Aliens" by Murray Leinster
First, he laid out a series of about thirty squares horizontally across a sheet of graph paper.
"Disturbing Sun" by Robert Shirley Richardson
A reference to the graph already given will indicate this rise.
"Report of the Committee of Inquiry into the Various Aspects of the Problem of Abortion in New Zealand" by David G. McMillan
Baker pointed soundlessly to the graph.
"The Great Gray Plague" by Raymond F. Jones
But that 'graph was never made.
"Astounding Stories of Super-Science April 1930" by Various
I've got the 'graphs right here!
"The Asses of Balaam" by Gordon Randall Garrett
We have a picture, or graph, as we say, of how this plate current varies.
"Letters of a Radio-Engineer to His Son" by John Mills
Another guest book is the "Hand-o-graph," in which the outline of the hand of each guest is kept.
"What Shall We Do Now?: Five Hundred Games and Pastimes" by Dorothy Canfield Fisher
The group was studying Sanborn tracings, continuous graphs showing the lines traced by the incoming signals.
"The Egyptian Cat Mystery" by Harold Leland Goodwin
The rates of rise and fall of temperature for each of the nine turtles considered are shown as a graph in Figure 23.
"Natural History of the Ornate Box Turtle, Terrapene ornata ornata Agassiz" by John M. Legler
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### In poetry:

by his beloved? We know all about graphs
and Darwin, enormous rooms no longer
superhumanise, but earnest
"Thanksgiving for a Habitat" by W H Auden

### In news:

Graph of the Week Graph of the Week: Idaho's Growing Obesity Problem.
Dealing with these lengths is a challenge, especially for large graphs .
Can We Graph Trends in Movie Genres.
Europe's Most Tragic Graph : Greek Youth Unemployment Hits 55.
Enhanced Placement Manager - faster querying through flexible placement algorithms - "Local Graphs " can be physically co-located to dramatically improve traversal speeds.
Why Cute Kitten Pictures Really Do Make You More Productive at Work—in 1 Graph .
The one graph you need to see before watching.
The wild performance spikes you see are the type that would set off the Juice-o- Graph 's alarms and red lights.
Google Refreshes Search, Expands Knowledge Graph .
How Romney Could Raise Taxes on 95% of the Country—in 1 Tall Graph .
Scary CDC graph shows state's whopping whooping cough increase.
Centers for Disease Control graph shows increase in pertussis in Washington state between early 2011 and June 2012.
This is one of the scariest graphs I've seen in a long time.
Win Three Great Guitar Accessories from Graph Tech.
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### In science:

If we deﬁne the diameter d of a graph to be the maximum distance between any two connected vertices in the graph, then it can be proven rigorously that the fraction of all possible graphs with n vertices and m edges for which d > c log n for some constant c tends to zero as n becomes large (Bollob´as, 1985).
Random graphs as models of networks
Random graph theory plays a large role in this analysis since movie ratings do not correspond to a particular graph, but rather a family of graphs.
A Connection-Centric Survey of Recommender Systems Research
If G is a partial function graph then each connected component of G is a cycle. A permutation graph G of a cyclus will be called a cyclus graph.
Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation
N −1 → x0 . G is a partial cyclus graph if it can be extended to a cyclus graph. A partial cyclus graph is proper if it is not a cyclus graph.
Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation
Small World (SW) graphs eﬃciently interpolate between regular and random graphs thanks to a small number pN of shortcuts (long-range connections) which are superimposed on a regular graph formed by N nodes.
Small-Worlds, Mazes and Random Walks
In Theorem 5.2 we show that any connected covering graph of a given connected graph can be written as a relative skew product graph of the base graph, a generalisation of the results in [GT, GT1].
Some intrinsic properties of simple graph \$C^*\$-algebras
The number of edges is between 0 (for the empty graph) and N (N − 1)/2 (for the complete graph). A component of a graph is a subset of connected vertices which are disconnect from the rest of the graph.
On large deviation properties of Erdos-Renyi random graphs
One was a typical random graph the other one for q < 1 (q > 1) a graph having minimal (maximal) number of components, i.e. a fully connected graph (a graph without edges).
On large deviation properties of Erdos-Renyi random graphs
On the other hand, the universality of a graph Γ in the sense of means that 1) any ﬁnite graph is isomorphic to a subgraph of Γ; 2) for every n, the group of automorphisms of the graph Γ acts transitively on the set of all subgraphs of Γ of order n isomorphic to an arbitrary given graph.
Random Metric Spaces and Universality
Graphs having 4N edges are actually considered as dense in the Graph Drawing community. 3Recall that a directed graph G is simply connected if its underlying non directed graph is connected.
Generating connected acyclic digraphs uniformly at random
We show that the resulting ensembles of random graphs strongly resemble those de ﬁned in random graphs with hidden color (CDRG), generalizing the known relation of the Feynman graphs of simple onedimensional integrals to random graphs with a given degree distribution.
Random Feynman Graphs
In the spirit of refs. [13, 14], we will consider the possibility of deﬁning ensembles of random graphs – random Feynman graphs – based on the Feynman graphs for such a system, with the statistical weight of each distinct graph taken to be proportional to the corresponding term in the perturbative expansion of Z .
Random Feynman Graphs
Now we want to interpret these Feynman graphs as random graphs in a multivariate version of RFG, with a statistical weight for each distinct graph proportional to the corresponding graph value as given by the Feynman rules.
Random Feynman Graphs
As we have already indicated in the Introduction, pseudo-random graphs are modeled after truly random graphs, and therefore mastering the edge distribution in random graphs can provide the most useful insight on what can be expected from pseudo-random graphs.
Pseudo-random graphs
Such graphs have been called regular quantum graphs by Severini and Tanner (2004); the name derives from the notation regular graphs for graphs which have the same number of incoming and outgoing arcs at every vertex and thus share the property that vertices are locally indistinguishable.
From quantum graphs to quantum random walks
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