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Property Graphs
A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated by directed relationships, and entities and relationships can have properties. In graph theory terms, a property graph is a directed multigraph, whose vertices represent entities and arcs represent relationships. Each arc has an identifier, a source node and a target node, and may have properties. Properties are key-value pairs where keys are character strings and values are numbers or character strings. They are analogous to attributes in entity-attribute-value and object-oriented modeling. By contrast, in RDF graphs, "properties" is the term for the arcs. This is why a clearer name is ''attributed graphs,'' or graphs'' with'' properties. This data model emerged in the early 2000s. Formal definition Building upon widely adopted definitions, a property graph/attributed graph can be defined by a 7-tuple (N, A, K, V, α, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Model
A data model is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities. For instance, a data model may specify that the data element representing a car be composed of a number of other elements which, in turn, represent the color and size of the car and define its owner. The corresponding professional activity is called generally ''data modeling'' or, more specifically, '' database design''. Data models are typically specified by a data expert, data specialist, data scientist, data librarian, or a data scholar. A data modeling language and notation are often represented in graphical form as diagrams. Michael R. McCaleb (1999)"A Conceptual Data Model of Datum Systems". National Institute of Standards and Technology. August 1999. A data model can sometimes be referred to as a data structure, especially in the context of programming languages. Data models are often complemented by function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Function
In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to . The subset , that is, the '' domain'' of viewed as a function, is called the domain of definition or natural domain of . If equals , that is, if is defined on every element in , then is said to be a total function. In other words, a partial function is a binary relation over two sets that associates to every element of the first set ''at most'' one element of the second set; it is thus a univalent relation. This generalizes the concept of a (total) function by not requiring ''every'' element of the first set to be associated to an element of the second set. A partial function is often used when its exact domain of definition is not known, or is difficult to specify. However, even when the exact domain of definition is known, partial functions are often used for simplicity or brevity. This is the case in calculus, where, for example, the quotien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Flow Problem
In Optimization (mathematics), optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from Glossary of graph theory#Direction, source s to Glossary of graph theory#Direction, sink t) is equal to the minimum capacity of an Cut (graph theory), s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem. History The maximum flow problem was first formulated in 1954 by Ted Harris (mathematician), T. E. Harris and F. S. Ross as a simplified model of Soviet railway traffic flow. In 1955, Lester R. Ford, Jr. and D. R. Fulkerson, Delbert R. Fulkerson created the first known algorithm, the Ford–Fulkerson algorithm.Ford, L.R., Jr.; Fulkerson, D.R., ''Flows in Networks'', Princeton University Press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A flow network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. As such, efficient algorithms for solving network flows can also be applied to solve problems that can be reduced to a flow network, including survey design, airline scheduling, image segmentation, and the matching prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Coloring
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a Graph (discrete mathematics), graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling. In its simplest form, it is a way of coloring the Vertex (graph theory), vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an ''edge coloring'' assigns a color to each Edge (graph theory), edges so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each Face (graph theory), face (or region) so that no two faces that share a boundary have the same color. Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Countable Set
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. In more technical terms, assuming the axiom of countable choice, a set is ''countable'' if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said to be countably infinite. The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers. A note on terminology Although the terms "countable" and "countably infinite" as def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Labeling
In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally, given a graph , a vertex labeling is a function of to a set of labels; a graph with such a function defined is called a vertex-labeled graph. Likewise, an edge labeling is a function of to a set of labels. In this case, the graph is called an edge-labeled graph. When the edge labels are members of an ordered set (e.g., the real numbers), it may be called a weighted graph. When used without qualification, the term labeled graph generally refers to a vertex-labeled graph with all labels distinct. Such a graph may equivalently be labeled by the consecutive integers , where is the number of vertices in the graph. For many applications, the edges or vertices are given labels that are meaningful in the associated domain. For example, the edges may be assigned weights representing the "cost" of trave ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
:Category:graph Algorithms
Graph algorithms solve problems related to graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph .... Computational problems in graph theory Combinatorial algorithms Algorithms {{CatAutoTOC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyponymy And Hypernymy
Hypernymy and hyponymy are the wikt:Wiktionary:Semantic relations, semantic relations between a generic term (''hypernym'') and a more specific term (''hyponym''). The hypernym is also called a ''supertype'', ''umbrella term'', or ''blanket term''. The hyponym names a subset, subtype of the hypernym. The semantic field of the hyponym is included within that of the hypernym. For example, "pigeon", "crow", and "hen" are all hyponyms of "bird" and "animal"; "bird" and "animal" are both hypernyms of "pigeon", "crow", and "hen". A core concept of hyponymy is ''type of'', whereas ''instance of'' is differentiable. For example, for the noun "city", a hyponym (naming a type of city) is "capital city" or "capital", whereas "Paris" and "London" are instances of a city, not types of city. Discussion In linguistics, semantics, general semantics, and ontology components, ontologies, hyponymy () shows the relationship between a generic term (hypernym) and a specific instance of it (hyponym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ockham's Razor
In philosophy, Occam's razor (also spelled Ockham's razor or Ocham's razor; ) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle of parsimony or the law of parsimony (). Attributed to William of Ockham, a 14th-century English philosopher and theologian, it is frequently cited as , which translates as "Entities must not be multiplied beyond necessity", although Occam never used these exact words. Popularly, the principle is sometimes paraphrased as "of two competing theories, the simpler explanation of an entity is to be preferred." This philosophical razor advocates that when presented with competing hypotheses about the same prediction and both hypotheses have equal explanatory power, one should prefer the hypothesis that requires the fewest assumptions, and that this is not meant to be a way of choosing between hypotheses that make different predictions. Similarl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instance (computer Science)
In computer science, an instance is an occurrence of a software element that is based on a type definition. When created, an occurrence is said to have been ''instantiated'', and both the creation process and the result of creation are called ''instantiation''. Examples ; Class instance: An object-oriented programming (OOP) object created from a class. Each instance of a class shares a data layout but has its own memory allocation. ; Computer instance: An occurrence of a virtual machine which typically includes storage, a virtual CPU. ; Polygonal model: In computer graphics, it can be instantiated in order to be drawn several times in different locations in a scene which can improve the performance of rendering since a portion of the work needed to display each instance is reused. ; Program instance: In a POSIX-oriented operating system, it refers to an executing process A process is a series or set of activities that interact to produce a result; it may occur once-only o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Database
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key concept of the system is the graph (or edge or relationship). The graph relates the data items in the store to a collection of nodes and edges, the edges representing the relationships between the nodes. The relationships allow data in the store to be linked together directly and, in many cases, retrieved with one operation. Graph databases hold the relationships between data as a priority. Querying relationships is fast because they are perpetually stored in the database. Relationships can be intuitively visualized using graph databases, making them useful for heavily inter-connected data. Graph databases are commonly referred to as a NoSQL database. Graph databases are similar to 1970s network model databases in that both represent general graphs, but network-model databases operate at a lower level of abstraction and lac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
