###### vertex

- Other terms used for the line graph include the covering graph , the derivative , the edge-to-vertex dual , the conjugate , the representative graph , and the ϑ-obrazom , as well as the edge graph , the interchange graph , the adjoint graph , and the derived graph . (wikipedia.org)
- Each vertex of the line graph is shown labeled with the pair of endpoints of the corresponding edge in the original graph. (wikipedia.org)
- Green vertex 1,3 is adjacent to three other green vertices: 1,4 and 1,2 (corresponding to edges sharing the endpoint 1 in the blue graph) and 4,3 (corresponding to an edge sharing the endpoint 3 in the blue graph). (wikipedia.org)
- The line graph of an edge-transitive graph is vertex-transitive . (wikipedia.org)
- if G is an edge-transitive graph that has at least five vertices, is not bipartite, and has odd vertex degrees, then L ( G ) is a vertex-transitive non-Cayley graph. (wikipedia.org)
- If a graph G has an Euler cycle , that is, if G is connected and has an even number of edges at each vertex, then the line graph of G is Hamiltonian . (wikipedia.org)
- A perfect elimination ordering in a graph is an ordering of the vertices of the graph such that, for each vertex v , v and the neighbors of v that occur after v in the order form a clique . (wikipedia.org)
- To list all maximal cliques of a chordal graph, simply find a perfect elimination ordering, form a clique for each vertex v together with the neighbors of v that are later than v in the perfect elimination ordering, and test whether each of the resulting cliques is maximal. (wikipedia.org)
- In computer science , graph traversal (also known as graph search ) refers to the process of visiting (checking and/or updating) each vertex in a graph . (wikipedia.org)
- Unlike tree traversal, graph traversal may require that some vertices be visited more than once, since it is not necessarily known before transitioning to a vertex that it has already been explored. (wikipedia.org)
- This may be accomplished by associating each vertex of the graph with a "color" or "visitation" state during the traversal, which is then checked and updated as the algorithm visits each vertex. (wikipedia.org)
- Both the depth-first and breadth-first graph searches are adaptations of tree-based algorithms, distinguished primarily by the lack of a structurally determined "root" vertex and the addition of a data structure to record the traversal's visitation state. (wikipedia.org)
- If each vertex in a graph is to be traversed by a tree-based algorithm (such as DFS or BFS), then the algorithm must be called at least once for each connected component of the graph. (wikipedia.org)
- This is easily accomplished by iterating through all the vertices of the graph, performing the algorithm on each vertex that is still unvisited when examined. (wikipedia.org)
- A graph G and a vertex v of G . (wikipedia.org)
- A maximum clique transversal of a graph is a subset of vertices with the property that each maximum clique of the graph contains at least one vertex in the subset. (wikipedia.org)
- The clique cover problem concerns finding as few cliques as possible that include every vertex in the graph. (wikipedia.org)
- A chordal graph is a graph whose vertices can be ordered into a perfect elimination ordering, an ordering such that the neighbors of each vertex v that come later than v in the ordering form a clique. (wikipedia.org)
- A cograph is a graph all of whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single vertex. (wikipedia.org)
- An interval graph is a graph whose maximal cliques can be ordered in such a way that, for each vertex v , the cliques containing v are consecutive in the ordering. (wikipedia.org)
- 1. An apex graph is a graph in which one vertex can be removed, leaving a planar subgraph. (wikipedia.org)
- A vertex in a connected graph whose removal would disconnect the graph. (wikipedia.org)
- A bipartite or multipartite graph is balanced if each two subsets of its vertex partition have sizes within one of each other. (wikipedia.org)
- The friendship graph F n can be constructed by joining n copies of the cycle graph C 3 with a common vertex. (wikipedia.org)
- class meets the requirements of the BGL Graph, Incidence Graph, Adjacency Graph, Vertex List Graph, and Edge List Graph concepts. (boost.org)
- Any type that meets the requirements of the Incidence Graph and Vertex List Graph concepts from the Boost Graph Library. (boost.org)

###### vertices of the graph

- It fills space in the sense that for any plane in 3-space, there exist vertices of the graph on both sides of the plane. (wikipedia.org)
- The adjacency matrix of a graph is a matrix whose rows and columns are both indexed by vertices of the graph, with a one in the cell for row i and column j when vertices i and j are adjacent, and a zero otherwise. (wikipedia.org)

###### acyclic

- 1. A graph is acyclic if it has no cycles. (wikipedia.org)
- An undirected acyclic graph is the same thing as a forest . (wikipedia.org)
- Directed acyclic graphs are less often called acyclic directed graphs. (wikipedia.org)
- 2. An acyclic coloring of an undirected graph is a proper coloring in which every two color classes induce a forest. (wikipedia.org)

###### dynamic graph algorithms

- We describe few dynamic graph problems that can be solved by dynamic graph algorithms, and finally we give a brief description of the methods used in dynamic algebraic graph algorithms, which are used for dynamic graphs using linear algebraic techniques. (springer.com)
- Eppstein D, Galil Z, Italiano GF, Nissenzweig A (1997) Sparsification a technique for speeding up dynamic graph algorithms. (springer.com)
- Henzinger MR, King V (1999) Randomized fully dynamic graph algorithms with polylogarithmic time per operation. (springer.com)
- A library for dynamic graph algorithms, and in particular dynamic connectivity. (haskell.org)

###### subset

- A clique , C , in an undirected graph G = ( V , E ) is a subset of the vertices , C ⊆ V , such that every two distinct vertices are adjacent. (wikipedia.org)

###### matchings

- Mucha M, Sankowski P (2006) Maximum matchings in planar graphs via Gaussian elimination. (springer.com)

###### line graph

- Hassler Whitney ( 1932 ) proved that with one exceptional case the structure of a connected graph G can be recovered completely from its line graph. (wikipedia.org)
- Various extensions of the concept of a line graph have been studied, including line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs. (wikipedia.org)
- The following figures show a graph (left, with blue vertices) and its line graph (right, with green vertices). (wikipedia.org)
- The line graph of a connected graph is connected. (wikipedia.org)
- A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one. (wikipedia.org)
- A maximum independent set in a line graph corresponds to maximum matching in the original graph. (wikipedia.org)
- for instance, the line graph of a Hamiltonian graph G is itself Hamiltonian, regardless of whether G is also Eulerian. (wikipedia.org)
- The prime symbol is often used to modify notation for graph invariants so that it applies to the line graph instead of the given graph. (wikipedia.org)
- α ′( G ) is the matching number of the graph, which equals the independence number of its line graph. (wikipedia.org)
- χ ′( G ) is the chromatic index of the graph, which equals the chromatic number of its line graph. (wikipedia.org)
- And each time you ask yourself a question "How to Draw a Line Graph easier and faster? (conceptdraw.com)

###### planar graph

- On cleaving a planar graph, manuscript, 1987. (springer.com)

###### dense

- Turán's theorem gives a lower bound on the size of a clique in dense graphs . (wikipedia.org)

###### Mathematics

- C. A. Barefoot and H. R. Entringer, "Vulnerability in graphs: a comparative survey," Journal of Combinatorial Mathematics and Combinatorial Computing , pp. 25-33, 1987. (hindawi.com)

###### Petersen

- A famous example is the Petersen graph , a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts. (wikipedia.org)

###### Proc

- Finding near optimal separators in planar graphs, In: Proc. (springer.com)

###### Harary

- F. Buckley and F. Harary, Distance in Graphs , 1990. (hindawi.com)

###### thesis

- G. Bacak Turan, Vulnerability parameters in graphs [Ph.D. thesis] , Ege University, 2010. (hindawi.com)

###### databases

- Develop, test, run, iterate and grow your enterprise applications with friction-less, agile development enabled by graph databases. (ibm.com)
- Graph databases come with enhanced connectivity of data and whiteboard friendly paradigm. (slideshare.net)
- This article aims to give an overview of the position of Graph Databases in the NOSQL-movement. (infoq.com)

###### connectivity

- Fiedler M (1973) Algebraic connectivity of graphs. (springer.com)

###### traversal

- Tree traversal is a special case of graph traversal. (wikipedia.org)
- Several special cases of graphs imply the visitation of other vertices in their structure, and thus do not require that visitation be explicitly recorded during the traversal. (wikipedia.org)
- A non-verbal description of three graph traversal algorithms: randomly, depth-first search, and breadth-first search. (wikipedia.org)
- As an example of this style, the Gremlin graph traversal language is presented. (slideshare.net)
- The language representation is then compiled to Gremlin bytecode to ultimately be executed by the/a Gremlin graph traversal machine. (slideshare.net)

###### theoretic

- Graphalyze-0.14.1.0: Graph-Theoretic Analysis library. (haskell.org)
- This general framework gives rise to a number of basic and widely studied graph routing problems, that have lead to the development of a rich toolkit of algorithmic techniques, as well as structural graph theoretic results. (princeton.edu)

###### data

- IBM Graph is designed to help you answer questions about large or complex networks of inter-related data. (ibm.com)
- It enhances the power of data connections by letting you store, query and visualize data points, connections and properties in a property graph. (ibm.com)
- Only a graph database provides constant read and write performance while the number and depth of data connections grow. (ibm.com)
- With just 3-4 simple lines of script, you can load your social media data, extract complex features, and generate a graph among arbitrary features. (microsoft.com)
- Graph is a family of rich, consistent REST APIs that provides vital connective tissue between applications, Azure cloud infrastructure, and IT resources and data stores. (microsoft.com)
- last year, Microsoft Principal Program Manager Yina Arenas explored the Graph APIs in her article, "Microsoft Graph: Gateway to Data and Intelligence" ( msdn.com/magazine/mt790189 ). (microsoft.com)
- The breadth of tools, SDKs, and documentation make Microsoft Graph the best way to access Microsoft data and insights. (microsoft.com)
- Plot a large number of points and updating one or more plots on the graph with new data, replacing the old plot with the new plot. (codeproject.com)
- Azure Cosmos DB - a multi-model database service - offers native support for Graphs, Document Data Models, Key-Value Pairs, and more. (infoq.com)
- Graph-Powered Machine Learning teaches you how to use graph-based algorithms and data organization strategies to develop superior machine learning applications. (manning.com)
- Graph-based machine learning is an incredibly powerful tool for any task that involves pattern matching in large data sets. (manning.com)
- By organizing and analyzing your data as graphs your applications work more fluidly with graph-centric algorithms like nearest neighbor or page rank where it's important to quickly identify and exploit relevant relationships. (manning.com)
- Modern graph data stores, like Neo4j or Amazon Neptune, are readily available tools that support graph-powered machine learning. (manning.com)
- Graph-Powered Machine Learning introduces you to graph technology concepts, highlighting the role of graphs in machine learning and big data platforms. (manning.com)
- With extensive experience in software development, software architecture, and data management, he has been a speaker at many conferences, such as Java One, Oracle Open World, and Graph Connect. (manning.com)
- Extracting data from graphs. (haskell.org)
- function in Data.GraphViz to determine potential graph layouts. (haskell.org)
- Powered by the Oracle Marketing Cloud and the Oracle Data Cloud, the powerful technology behind the Oracle ID Graph™ unites disparate data sources to form a unique, singular profile of consumers in the Oracle Data Management Platform. (oracle.com)
- With tools powered by the Oracle ID Graph to unify data across channels. (oracle.com)
- The Oracle ID Graph establishes and validates connections between IDs that enable the transport of data from one ID space to another, for the purposes of targeting or measurement applications. (oracle.com)

###### Moser

- According to a result of Moon & Moser (1965) , a graph with 3 n vertices can have at most 3 n maximal cliques. (wikipedia.org)

###### topologically

- Two periodic graphs are often called topologically equivalent if they are isomorphic, although not necessarily homotopic . (wikipedia.org)

###### cycles

- If the graph contains cycles, how can there exist allowed execution orders for your files? (stackoverflow.com)
- Yes, a topological sort is not possible if a graph contains cycles. (stackoverflow.com)

###### Methods

- New Methods to Color Vertices of a Graph," Communications of the ACM 22, 251-256. (springer.com)

###### 2018

- Huan J. (2018) Frequent Graph Patterns. (springer.com)

###### Extract

- Extract planar graphs and hyper-graphs of co-occurrence relationships, and tracks contextual statistics for each relationship. (microsoft.com)

###### corresponds

- The opposite of a clique is an independent set , in the sense that every clique corresponds to an independent set in the complement graph . (wikipedia.org)

###### maximum clique

- A maximum clique of a graph, G , is a clique, such that there is no clique with more vertices. (wikipedia.org)
- Moreover, the clique number ω( G ) of a graph G is the number of vertices in a maximum clique in G . (wikipedia.org)

###### Given

- the task of finding whether there is a clique of a given size in a graph (the clique problem ) is NP-complete , but despite this hardness result, many algorithms for finding cliques have been studied. (wikipedia.org)
- PhyloGrapher is a drawing tool that generates custom graphs for a given set of elements. (debian.org)
- is indeed present in the given graph. (haskell.org)
- Create a new communicator whose topology is described by the given graph. (boost.org)
- In a typical routing problem, we are given a graph G, and a collection (s_1,t_1),…,(s_k,t_k) of pairs of vertices, called demand pairs, that we would like to route. (princeton.edu)

###### functions

- Specifically, we'll use Excel functions and graphing to explore the normal distribution family. (lynda.com)
- In this issue of MSDN Magazine, Mike Ammerlaan writes " Build the API to Your Organization with Microsoft Graph and Azure Functions ," in which he describes how the new Azure Functions Binding Extensions can be used to automate common tasks and processes. (microsoft.com)
- Our approach is based on characterizing the feasibility of graph watermarking in terms of keygen, marking, and identification functions defined over graph families with known distributions. (springer.com)