Graph of a relation
Der Begriff Graph of a relation ist im englisch-sprachigen Wikipedia aufgeführt. Dort heißt es dazu:

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms correspondence, dyadic relation and 2-place relation are synonyms for binary relation.
An example is the "divides" relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p (and not with any integer that is not a multiple of p). In this relation, for instance, the prime 2 is associated with numbers that include −4, 0, 6, 10, but not 1 or 9; and the prime 3 is associated with numbers that include 0, 6, and 9, but not 4 or 13.
Binary relations are used in many branches of mathematics to model concepts like "is greater than", "is equal to", and "divides" in arithmetic, "is congruent to" in geometry, "is adjacent to" in graph theory, "is orthogonal to" in linear algebra and many more. The concept of function is defined as a special kind of binary relation. Binary relations are also heavily used in computer science.
A binary relation is the special case n = 2 of an n-ary relation R ⊆ A1 × … × An, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain Aj of the relation.
In some systems of axiomatic set theory, relations are extended to classes, which are generalizations of sets. This extension is needed for, among other things, modeling the concepts of "is an element of" or "is a subset of" in set theory, without running into logical inconsistencies such as Russell's paradox.

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Relation (Mathematik) – Wikipedia
Eine Relation ist allgemein eine Beziehung, die zwischen Dingen bestehen ... Zielmenge in die Definition mit ein, obige Teilmenge wird dann der Graph G_R ...
de.wikipedia.org/wiki/Relation_(Mathematik)
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Functions versus Relations - Purplemath
This characteristic of non-functions was noticed by I-don't-know-who, and was codified in "The Vertical Line Test": Given the Graph of a relation, if you can draw a ...
www.purplemath.com/modules/fcns.htm
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1.2. GRAPHS OF RELATIONS Graphs of relations as sets - Tutor ...
1.2.1. DEFINITION. The Graph of a relation R is the set of all points (x, y) in a coordinate plane such that x is related to y through the relation R. 1.2.2. EXAMPLE.
www.tutor-homework.com/Math_Help/college_algebra/m1l2notes.pdf
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Relationen und Graphen - FernUniversität in Hagen
21. Mai 2011 ... Graphen. Studientag zur Algorithmischen Mathematik. Relationen und Graphen. Winfried Hochstättler. Diskrete Mathematik und Optimierung.
www.fernuni-hagen.de/videostreaming/dmo/201105/studientag_teil2.pdf
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SparkNotes: Algebra II: Functions: Relations and Functions
A relation is a set of inputs and outputs, often written as ordered pairs (input, output). We can also represent a relation as a mapping diagram or a graph.
www.sparknotes.com/math/algebra2/functions/section1.rhtml
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Math Planet - Graph functions and relations
In order to graph a linear equation we work in 3 steps: First we solve the equation for y. Second we make a table for our x- and y-values. From the x values we ...
www.mathplanet.com/education/algebra-2/how-to-graph-functions-and-linear-equations/graph-functions-and-relations
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Graphen einer Relation - Uni-Protokolle.de
Hallo in einer Hausaufgabe soll ich den Graphen folgender Relation R={(x,y)| |y| =|x|}RxR zeichnen. Leider kann ich mit dem Ausdruck Relation ...
www.uni-protokolle.de/foren/viewt/67142,0.html
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Graphing Functions and Relations - Hotmath
Consider the following relation on the set of whole numbers between 1 and 10. If x and y are both multiples of 3, then they are related. Otherwise it is not. Graph ...
hotmath.com/help/gt/genericalg1/section_2_2.html
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Graphical relations and functions | Recognizing ... - Khan Academy
Determine whether the points on this graph represent a function. Now just as a refresher a function is; really just an association between members of a set that ...
www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-relationships-functions/cc-8th-function-intro/v/graphical-relations-and-functions
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Graphing Relations - Shmoop
Graph the relation {(1, 2), (3, 4)}. This problem is telling you to graph the ordered pair (1, 2) and the ordered pair (3, 4) in the same picture. A treasure map ...
www.shmoop.com/functions/graphing-relations.html
Suchergebnisse für "Graph of a relation"
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Graph of a relation in der Wissenschaft
[PDF]Graphen Teil 1
Graphen eignen sich zur Modellierung für ein breites Aufgabenspektrum. ... Kanten: Beziehung zwischen je zwei Objekten, 2-stellige Relation über Knoten.
Forum "Uni-Sonstiges" - Graphen und Äquivalenzrelation - MatheRaum ...
Forum "Uni-Sonstiges" - Graphen und Äquivalenzrelation - MatheRaum - Offene ... Graphen und Äquivalenzrelation: Frage (beantwortet) ...
[PDF]Graphen - Fachbereich Mathematik und Informatik - Philipps ...
H. Peter Gumm, Philipps-Universität Marburg. Prakt. ... Ein Graph definiert eine zweistellige Relation R ⊆ V × V ... Umgekehrt definiert jede zweistellige Relation.
Economics Basics: Supply and Demand | Investopedia
The demand relationship curve illustrates the negative relationship between price and quantity demanded. The higher the price of a good the lower the quantity ...
[PDF]Relationen, Graphen, Inferenz (PDF) - GWDG
Relationen, Graphen und Inferenz. Relationen ... (b) Jede irreflexive und transitive Relation < auf M ist auch ..... (genaue Quellenangaben siehe http://www .uni-.
[PDF]Notationen für Relationen und Graphen
Notationen für Relationen und Graphen. In diesem Text werden die in der Veranstaltung. ” Datengewinnung und ihre wissenschaftstheoretischen Grundlagen“ ...
[PDF]TECHNISCHE UNIVERSITÄT DRESDEN Fakultät Mathematik und ...
Im einzelnen sollte folgendes untersucht werden: • Darstellung von binären Relationen als Graphen,. • Anzahl der binären Relationen auf einer n- elementigen ...
[PDF]1.3 – Relationen und Graphen
Informatik I. 1 Theorie. 1.3 – Relationen und Graphen. Eine (zweistellige homogene) Relation R auf einer Menge V ist eine Teilmenge des kartesischen ...
Gerichteter Graph – Wikipedia
Die Mängel sind unter Diskussion:Gerichteter Graph beschrieben. Wenn du diesen Baustein .... 108, Cambridge University Press, 2006, ISBN 9780521865654.
[PDF]A Comparison of SLAM Algorithms Based on a Graph of Relations
A Comparison of SLAM Algorithms Based on a Graph of Relations. Wolfram ... All authors are with the University of Freiburg, Dept. of Computer. Science ...
Bücher zum Begriff Graph of a relation
Mathematische Grundlagen Der Ingenieurinformatik
Mathematische Grundlagen Der Ingenieurinformatik
Peter Jan Pahl, Rudolf Damrath, 2000
8. GRAPHEN. 8.1 EINFÜHRUNG Der Aufbau der Mathematik beruht auf der Verknüpfung von Mengen durch Relationen. Die Mengen enthalten gegebene Elemente. Die Relationen sind ebenfalls Mengen und enthalten Tupel, die mit ...
Der Graf der Graphen: Kriminalistische Verwicklungen mit mathematischer Pointe
Der Graf der Graphen: Kriminalistische Verwicklungen mit mathematischer Pointe
Alain Hertz, Micaela Krieger-Hauwede und Ines Laue von Vieweg+Teubner Verlag, 2011
Rätselhafte Ereignisse sind Gegenstand der Ermittlungen von Maurice Manori -- Kriminalinspektor alias Agrapheur (Graf der Graphen). Den Spitznamen verdankt er seinen ebenso effizienten wie unkonventionellen Methoden. In der Tat verfügt er über ein furchterregendes Werkzeug zur Ergreifung der Schuldigen in seinen Kriminalfällen: die Graphentheorie. ...
Calculus with Analytic Geometry
Calculus with Analytic Geometry
Murray H. Protter, Philip E. Protter, 1988
ASYMPTOTES DEFINITIONS The solution set of an equation in two unknowns, say x and y, is called a relation. The domain of a relation is the set of all numbers x0 such that the vertical line x = x0 intersects the graph of the relation. The range  ...
Mathematik - Physik - Chemie: Formelsammlung
Mathematik - Physik - Chemie: Formelsammlung
Alois Einhauser und Christian Hörter von Cornelsen Verlag, 2008
Informationen zum Titel: Diese Formelsammlung ist an die Vorgaben des Kultusministeriums angepasst. Sie umfasst alle Schwerpunktthemen der Fächer Mathematik, Physik und Chemie: Die wichtigsten mathematischen Definitionen, Formeln und Rechenregeln aus den Bereichen Algebra, Funktionen, Trigonometrie, Geometrie, Vektoren, Abbildungen und Stochastik A...
Conceptual Structures: Integration and Interfaces: 10th ...
Conceptual Structures: Integration and Interfaces: 10th ...
Uta Priss, Dan Corbett, Galia Angelova, 2002
Contextual Logic of Relations (CLR) is based on Formal Concept Analysis (FCA) and Peircean Algebraic Logic (PAL). The aim of the paper is to introduce relation graphs as an algebraic structure for representing relations and operations on ...
Taschenbuch mathematischer Formeln für Ingenieure und Naturwissenschaftler
Taschenbuch mathematischer Formeln für Ingenieure und Naturwissenschaftler
Hans-Jochen Bartsch von Carl Hanser Verlag GmbH & Co. KG, 2014
Das umfassende Taschenbuch zur Mathematik ist ein kompaktes und kompetentes Nachschlagewerk für Studierende technischer Fachrichtungen an Hochschulen und Universitäten und für den Praktiker zum Auffrischen der Kenntnisse.In der 23. Auflage werden die Kapitel Gleichungen und Funktionen überarbeitet.Bisher weit über eine Million verkaufter Exemplare ...
Essentials of Discrete Mathematics
Essentials of Discrete Mathematics
David James Hunter, 2009
Draw the graph associated with the < relation on X. Should this graph be directed or undirected? 2. Let X = {0,1,2,3,4}. Define a relation R on X such that x R y if x + y = 4. Draw the graph associated with this relation. Should this graph be ...
Einführung in LabVIEW
Einführung in LabVIEW
Wolfgang Georgi und Ergun Metin von Carl Hanser Verlag GmbH & Co. KG, 2012
LabVIEW ist ein graphisches Programmiersystem und findet in der Messtechnik, der Regelungstechnik und der Automatisierungstechnik seine Hauptanwendungsgebiete. Dieses Lehrbuch führt in das Programmieren mit LabVIEW ein. Es richtet sich an Studierende, bietet aber ebenso Ingenieuren einen guten Einstieg für die Weiterbildung. Auch interessierte Schü...
Introduction to Discrete Mathematics with ISETL
Introduction to Discrete Mathematics with ISETL
Ed Dubinsky, 1996
There are many more properties that a relation could have. Some of these properties come directly from the graphs and are better understood as questions about graphs. But there are two properties we want to include here. A relation is called ...
Mathematik für Informatiker: Band 1: Diskrete Mathematik und Lineare Algebra (eXamen.press)
Mathematik für Informatiker: Band 1: Diskrete Mathematik und Lineare Algebra (eXamen.press)
Gerald Teschl von Springer, 2013
In diesem Lehrbuch werden die mathematischen Grundlagen exakt und dennoch anschaulich und gut nachvollziehbar vermittelt. Sie werden durchgehend anhand zahlreicher Musterbeispiele illustriert, durch Anwendungen in der Informatik motiviert und durch historische Hintergründe oder Ausblicke in angrenzende Themengebiete aufgelockert. Am Ende jedes Kapi...
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Blog-Einträge zum Begriff
Graph of a relation
Evolution: Demographics, Personas and the Relationship Graph | The Nimble Blog
There are interesting and useful ways to use a new form of search and the data it can provide. We’re not there yet, but with the growing popularity of graph databases, the ideas behind the Social Graph are about to become very useful to sales and marketing teams.
www.nimble.com/blog/evolution-demographics-personas-and-the-relationship-graph/
Relationship Management: The Key To Flourishing in the Social Graph | The Contactually Blog
Your social graph is important. Learn how relationship management can get you get the most from it.
blog.contactually.com/2013/09/relationship-management-the-key-to-flourishing-in-the-social-graph/
The Formation of Love
www.facebook.com/notes/facebook-data-science/the-formation-of-love/10152064609253859
Graph vs. Relationship Databases | OrgVue Blog
So, having gotten my head around relational databases and feel a small quantum of expertise in them, it was quite a surprise when the OrgVue team informed me that we would take inspiration from graph databases in order to solve the Org Design problem I had laid out.
blog.orgvue.com/graph-vs-relationship-databases/
Neo4j Blog: Modeling categories in a graph database
Storing hierarchical data can be a pain when using the wrong tools. However, the Neo4j open source graph database is a good fit to this kind of problems, and this post will show you an example of how it can be used.
blog.neo4j.org/2010/03/modeling-categories-in-graph-database.html
Neo4j Blog: Fun with Beer - and Graphs
I make no excuses: My name is Rik van Bruggen and I am a salesperson. I think it is one of the finest and nicest professions in the world, and I love what I do.
blog.neo4j.org/2013/01/fun-with-beer-and-graphs.html
Working hours: Get a life | The Economist
Authoritative weekly newspaper focusing on international politics and business news and opinion.
www.economist.com/blogs/freeexchange/2013/09/working-hours
Social Media Aktuell #4: Facebook Graph Search, Tools, Blogger Relations & mehr « Michael Ehlers Blog
Facebook und der Graph Search Aktuell befindet sich die neue Graph Search Funktion von Facebook zwar noch in einer Beta-Version, jedoch wird es nicht mehr lange dauern und die neue Suchfunktion kommt. Doch was bedeutet das für den Nutzer und ganz besonders für Unternehmen?
www.blog.michael-ehlers.de/social-media-aktuell-4-facebook-graph-search-tools-blogger-relations-mehr/
Multi-way Clustering on Relation Graphs - CSE User Home Pages
www-users.cs.umn.edu/~banerjee/papers/07/mrgc.pdf
Quick Glance at Neo4j Cypher Queries for Sample Graph Database - Technical Blogs : Technical Blogs
Quick Glance at Neo4j Cypher Queries for Sample Graph Database Piyas De • May 24, 2013 • 3 Comments ]]> // ]]> We have tried to show different Neo4j Cypher Queries to show different capabilities of graph database. To start with graph database preliminary concepts, read Preliminary Concepts of Graph Database. .We have given below the cypher queries, which are based on a model – which is described in Case Study in Graph Database in Context of Neo4j Cypher Query. Installation - Install Neo4J from http://www.neo4j.org/download Starting Neo4j Server in Windows - - neo4j.bat start Then go to browser at the address – http://localhost:7474 Now the cypher queries, which we have tested on the Data Console which is in relation to the mentioned model. Creating Nodes - CREATE (user {entitytype:’user’, name : ‘bill’}) return user; CREATE (company {entitytype:’company’, name : ‘CTS’}) return company; CREATE (project {entitytype:’project’, name : ‘ABC Insurance’}) return project; CREATE (skill {entitytype:’skill’, name : ‘HTML, CSS’}) return skill; Some of the Nodes creation examples are shown here. Creating Relationships - START user=node(1), company=node(9) CREATE relation = user-[:WORKS_AT]->company return relation; START user=node(7), company=node(9) CREATE relation = user-[:FOLLOWS]->company return relation; START user=node(5), skill=node(12) CREATE relation = user-[:HAS_SKILL]->skill return relation; START user=node(6), seconduser=node(7) CREATE relation = user-[:FRIEND]->seconduser return relation; START user=node(6), work=node(11) CREATE relation = user-[:CURRENT_ENGADGEMENT]->work return relation; START user=node(6), work=node(11) CREATE relation = user-[:CURRENT_ENGADGEMENT]->work return relation; START company=node(9), project=node(11) CREATE relation = company-[:EXECUTING_UNDER]->project return relation; Some of the relation creation examples are shown here. Removing node - START nullnode=node(0), DELETE nullnode; // Delete a Node Fetching Nodes and Relationships - start n = node(*) return n;// See all the nodesstart r = relationship(*) return r; //see all the relationships start n = node:node_auto_index(name = ‘john’) return n;// Selecting particular user –>Selecting Data by Indexes START n=node(*) WHERE has(n.name) RETURN n; // Selecting those nodes where we have name properties START n=node(*) WHERE has(n.name) and (n.entitytype = ‘skill’) RETURN n; // Selecting nodes where entitytype = ‘Skill’ index –indexes // To Get the Indexes in nodes and relationships START n=node(*) WHERE has(n.name) and n.name =~ ‘j.*’ return n; //Selecting nodes from indexes where node name starts with “j” START n=node(*) WHERE has(n.name) and n.name =~ ‘.*j.*’ return n; //Selecting nodes from indexes where node name contains “j” start n = node(6) match(n)–(x) return x; //return all the related nodes with node 6 start n = node:node_auto_index(name=’andrew’) match(n)–(x) return x; //return all the related nodes with node name = ‘andrew’ start n = node:node_auto_index(name=’andrew’) match(n)(x) return x; // return all nodes which are having outbound relationship with ‘andrew’ // Note : Here all entitytype (skill, project, user, company) to which andrew is having outbound relationship will return START n=node:node_auto_index(name=’andrew’) MATCH (n)-[:WORKS_AT]->(x) RETURN x; //Match by relationship type and outbound nodes START n=node:node_auto_index(name=’linda’) MATCH (n)-[:FRIEND]->(x) RETURN x; // Here result will be ‘andrew’ who is outbound relationship to ‘linda’ START n=node:node_auto_index(name=’linda’) MATCH (n)() return r; // Match by relationship type and use an identifier START a=node:node_auto_index(name=’andrew’) MATCH (a)-[:WORKS_AT]->(b)company) RETURN persons; // Those persons will be returned who are not related to ‘IBM’riend START persons=node(*), company=node:node_auto_index(name=’IBM’) WHERE has(persons.name) and (persons.entitytype=’user’) and (persons–>company) RETURN persons; // Those persons will be returned who are has relation to ‘IBM’ (here note the ‘WORKS_AT’ and ‘FOLLOWS’ relationship) START persons=node(*), company=node:node_auto_index(name=’IBM’) WHERE has(persons.name) and (persons.entitytype=’user’) and (persons-[:WORKS_AT]->company) RETURN persons; // Those persons will be returned who are has relation to ‘IBM’ (Only ‘WORKS_AT’ relationship) START me=node:node_auto_index(name=’andrew’) MATCH me–>friend where (friend.entitytype=’user’) RETURN count(friend),friend; // Return only those users who are outbound to ‘andrew’ START me=node:node_auto_index(name=’andrew’) MATCH me.
www.phloxblog.in/neo4j-cypher-queries-sample-graph-database/
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