In the world migration graph, the numbers on each directed edge are data.
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A pair is connected with a directed edge (arrow), which is "one-sided" like on a one-way street sign.
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The objects are shown as points (or vertices) and the pair relationship is shown with an arrow (a directed edge).
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In addition, oppositely directed edge states carry opposite spin projections.
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Jasper, Alberta (2011). Gwaai Edenshaw is a Haida artist and filmmaker from Canada. Along with Helen Haig-Brown, he co-directed Edge of the Knife (), the first Haida language feature film.
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This allows the two vertices to have explicit names (start and end), and this gives faces explicit names as well (left and right, relative to a person standing on start and looking in the direction of end). The four edges are also given names, based on the vertices and faces: start-left, start-right, end-left, and end-right. A directed edge can be reversed to generate the edge in the opposite direction. Iterating around a particular face only requires having a single directed edge to which that face is on the left (by convention) and then walking through all of the start-left edges until the original edge is reached.
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Peaks in the spectrum are transformed into vertices in a graph called "spectrum graph". If two vertices have the same mass difference of one or several amino acids, a directed edge will be applied. The SeqMS algorithm, Lutefisk algorithm, Sherenga algorithm are some examples of this type.
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A single comparator gate. A comparator circuit is a network of wires and gates. Each comparator gate, which is a directed edge connecting two wires, takes its two inputs and outputs them in sorted order (the larger value ending up in the wire the edge is pointing to). The input to any wire can be either a variable, its negation, or a constant.
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This is represented using arrow notation; a → b indicates that a reduces to b. Intuitively, this means that the corresponding graph has a directed edge from a to b. If there is a path between two graph nodes c and d, then it forms a reduction sequence. So, for instance, if c → c’ → c’’ → ... → d’ → d, then we can write c d, indicating the existence of a reduction sequence from c to d.
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A roadmap G = (V,E) is a directed graph. Each vertex v is a randomly sampled conformation in C. Each (directed) edge from vertex vi to vertex vj carries a weight Pij , which represents the probability that the molecule will move to conformation vj , given that it is currently at vi. The probability Pij is 0 if there is no edge from vi to vj. Otherwise, it depends on the energy difference between conformations.
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He used these to analyse circuits containing mutual couplings and active networks. The weight of a directed edge in these graphs represents a gain, such as possessed by an amplifier. In general, signal-flow graphs, unlike the regular directed graphs described above, do not correspond to the topology of the physical arrangement of components. The second approach is to extend the classical method so that it includes mutual couplings and active components.
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The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y.
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If there are n concurrent threads running, a process graph models the execution of n concurrent threads and their trajectories through an n dimensional Cartesian plane. The origin of the graph corresponds to the initial state where none of the threads have completed an instruction. Each directed edge corresponds to the execution of an instruction and transition to other. Valid edges can either go up or right because programs cannot run backward for the edges to left or down.
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This results in a directed edge from T1 to T2 (as T1 has R(A) before T2 having W(A)). # For each case in S where Tj executes a write_item(X) after Ti executes a write_item(X), create an edge (Ti → Tj) in the precedence graph. This results in directed edges from T2 to T1, T2 to T3 and T1 to T3. # The schedule S is serializable if and only if the precedence graph has no cycles.
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However, food-web models based on a niche axis do not reproduce realistic trophic coherence, which may mean either that this explanation is insufficient, or that several niche dimensions need to be considered. Network of concatenated words from Green Eggs and Ham, by Dr Seuss. If word 1 appears immediately before word 2 in at least one sentence in the text, a directed edge (arrow) is placed from word 1 to word 2. The height of each word is proportional to its trophic level.
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Cyclomatic complexity is a software metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent paths through a program's source code. It was developed by Thomas J. McCabe, Sr. in 1976. Cyclomatic complexity is computed using the control flow graph of the program: the nodes of the graph correspond to indivisible groups of commands of a program, and a directed edge connects two nodes if the second command might be executed immediately after the first command.
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In this directed network, reaction A has a directed edge towards reaction B if the product of the former enters the latter reaction as a substrate or co-factor. To select important nodes that could serve as drug targets, we might think of selecting high in-degree nodes (hubs; nodes with many incoming edges). It was shown however[2], that targeting hub proteins with many vital functions may unintentionally harm the living cell as well. A PageRank-based scoring method could detect important nodes that are not hubs and therefore might be better drug targets.
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A tournament is a directed graph with one directed edge between each pair of vertices. Intuitively, a tournament can be used to model a round-robin sports competition, by drawing an edge from the winner to the loser of each game in the competition. A tournament is called strongly connected or strong if and only if it cannot be partitioned into two nonempty subsets L and W of losers and winners, such that every competitor in W beats every competitor in L., Corollary 5b. Every strong tournament is pancyclic, Theorem 7.
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The initial formulation of the retiming problem as described by Leiserson and Saxe is as follows. Given a directed graph G:=(V,E) whose vertices represent logic gates or combinational delay elements in a circuit, assume there is a directed edge e:=(u,v) between two elements that are connected directly or through one or more registers. Let the weight of each edge w(e) be the number of registers present along edge e in the initial circuit. Let d(v) be the propagation delay through vertex v.
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A tournament is a directed graph (digraph) obtained by assigning a direction for each edge in an undirected complete graph. That is, it is an orientation of a complete graph, or equivalently a directed graph in which every pair of distinct vertices is connected by a directed edge with any one of the two possible orientations. Many of the important properties of tournaments were first investigated by in order to model dominance relations in flocks of chickens. Current applications of tournaments include the study of voting theory and social choice theory among other things.
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An input gate computes the polynomial it is labeled by. A sum gate v computes the sum of the polynomials computed by its children (a gate u is a child of v if the directed edge (v,u) is in the graph). A product gate computes the product of the polynomials computed by its children. Consider the circuit in the figure, for example: the input gates compute (from left to right) x_1, x_2 and 1, the sum gates compute x_1 + x_2 and x_2 + 1, and the product gate computes (x_1 + x_2) x_2 (x_2 +1).
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Given a DFA, the problem of determining if it has a synchronizing word can be solved in polynomial time using a theorem due to Ján Černý. A simple approach considers the power set of states of the DFA, and builds a directed graph where nodes belong to the power set, and a directed edge describes the action of the transition function. A path from the node of all states to a singleton state shows the existence of a synchronizing word. This algorithm is exponential in the number of states.
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Distributed scientists can collaborate on conducting large scale scientific experiments and knowledge discovery applications using distributed systems of computing resources, data sets, and devices. Scientific workflow systems play an important role in enabling this vision. More specialized scientific workflow systems provide a visual programming front end enabling users to easily construct their applications as a visual graph by connecting nodes together, and tools have also been developed to build such applications in a platform-independent manner. Each directed edge in the graph of a workflow typically represents a connection from the output of one application to the input of the next.
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A nearest neighbor graph of 100 points in the Euclidean plane. The nearest neighbor graph (NNG) for a set of n objects P in a metric space (e.g., for a set of points in the plane with Euclidean distance) is a directed graph with P being its vertex set and with a directed edge from p to q whenever q is a nearest neighbor of p (i.e., the distance from p to q is no larger than from p to any other object from P). In many discussions the directions of the edges are ignored and the NNG is defined as an ordinary (undirected) graph.
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In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations. The Coates graph Gc(A) associated with an n × n matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry aji ≠ 0 then there is a directed edge from node i to node j with weight aji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.
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Each component has a number of parameters that can be set by the user and also a number of input and output ports for receiving and transmitting data. Each directed edge in the graph represents a connection from an output port, namely the tail of the edge, to an input port, namely the head of the edge. A port is connected if there is one or more connections from/to that port. In addition, each node in the graph provides metadata describing the input and output ports of the component, including the type of data that can be passed to the component and parameters of the service that a user might want to change.
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An implication graph. Its skew symmetry can be realized by rotating the graph through a 180 degree angle and reversing all edges. An instance of the 2-satisfiability problem, that is, a Boolean expression in conjunctive normal form with two variables or negations of variables per clause, may be transformed into an implication graph by replacing each clause \scriptstyle u\lor v by the two implications \scriptstyle(\lnot u)\Rightarrow v and \scriptstyle(\lnot v)\Rightarrow u. This graph has a vertex for each variable or negated variable, and a directed edge for each implication; it is, by construction, skew-symmetric, with a correspondence σ that maps each variable to its negation.
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Recent research investigate the connection between network topology and the flow efficiency of the transportation. The flow is often generated or influenced by local gradients of a scalar, for example: electric current driven by a gradient of electric potential; in the information networks, properties of nodes will generate a bias in the way of information is transmitted from a node to its neighbors. This idea motivated the approach through gradient networks which studies flow efficiency on the network when the flow is driven by gradients of a scalar field distributed on the network Fig.2. The gradient at node i is a directed edge pointing towards the largest increase of the scalar potential in the node's neighborhood.
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In this case each matrix can be encoded as a directed edge of a graph with n vertices. So all matrices together give a graph on n vertices with 2n directed edges. The identity holds provided that for any two vertices A and B of the graph, the number of odd Eulerian paths from A to B is the same as the number of even ones. (Here a path is called odd or even depending on whether its edges taken in order give an odd or even permutation of the 2n edges.) Swan showed that this was the case provided the number of edges in the graph is at least 2n, thus proving the Amitsur–Levitzki theorem.
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This is often denoted as just: : The above definition is extended to directed graphs. Then, for a homomorphism f : G → H, (f(u),f(v)) is an arc (directed edge) of H whenever (u,v) is an arc of G. There is an injective homomorphism from G to H (i.e., one that never maps distinct vertices to one vertex) if and only if G is a subgraph of H. If a homomorphism f : G → H is a bijection (a one-to-one correspondence between vertices of G and H) whose inverse function is also a graph homomorphism, then f is a graph isomorphism. Covering maps are a special kind of homomorphisms that mirror the definition and many properties of covering maps in topology.
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In the original presentation, serial computations were represented as nodes as well, and a directed edge represented the relation "is followed by". As an example, consider the following trivial fork–join program in Cilk-like syntax: function f(a, b): c ← fork g(a) d ← h(b) join return c + d function g(a): return a × 2 function h(a): b ← fork g(a) c ← a + 1 join return b + c The function call gives rise to the following computation graph: fork–join computation. In the graph, when two edges leave a node, the computations represented by the edge labels are logically parallel: they may be performed either in parallel, or sequentially. The computation may only proceed past a join node when the computations represented by its incoming edges are complete.
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In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time.
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In this problem, one must choose time slots for the edges of a wireless communications network so that each node of the network can communicate with each neighboring node without interference. Using a strong edge coloring (and using two time slots for each edge color, one for each direction) would solve the problem but might use more time slots than necessary. Instead, they seek a coloring of the directed graph formed by doubling each undirected edge of the network, with the property that each directed edge has a different color from the edges that go out from and from the neighbors of . They propose a heuristic for this problem based on a distributed algorithm for -edge-coloring together with a postprocessing phase that reschedules edges that might interfere with each other.
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Time-order between two operations can be represented by an ordered pair of these operations (e.g., the existence of a pair (OP1, OP2) means that OP1 is always before OP2), and a schedule in the general case is a set of such ordered pairs. Such a set, a schedule, is a partial order which can be represented by an acyclic directed graph (or directed acyclic graph, DAG) with operations as nodes and time-order as a directed edge (no cycles are allowed since a cycle means that a first (any) operation on a cycle can be both before and after (any) another second operation on the cycle, which contradicts our perception of Time). In many cases, a graphical representation of such a graph is used to demonstrate a schedule.
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Shortest path algorithms are applied to automatically find directions between physical locations, such as driving directions on web mapping websites like MapQuest or Google Maps. For this application fast specialized algorithms are available. If one represents a nondeterministic abstract machine as a graph where vertices describe states and edges describe possible transitions, shortest path algorithms can be used to find an optimal sequence of choices to reach a certain goal state, or to establish lower bounds on the time needed to reach a given state. For example, if vertices represent the states of a puzzle like a Rubik's Cube and each directed edge corresponds to a single move or turn, shortest path algorithms can be used to find a solution that uses the minimum possible number of moves.
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A raffinement on the above definition can be made, resulting in the concept of acyclic agreement forest. An agreement forest for two -trees and is said to be acyclic if each of its tree components can be numbered in such a way that if the root of one component is an ancestor of the root of another component in either or , then the number assigned to is lower than the number assigned to . Another characterization of acyclicity in agreement forest is to consider the directed graph that has vertex set and a directed edge if and only if and at least one of the two following conditions hold: # the root of is an ancestor of the root of in # the root of is an ancestor of the root of in The directed graph is called the inheritance graph associated with the agreement forest , and we call acyclic if has no directed cycle.
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A gene co-expression network constructed from a microarray dataset containing gene expression profiles of 7221 genes for 18 gastric cancer patients A gene co-expression network (GCN) is an undirected graph, where each node corresponds to a gene, and a pair of nodes is connected with an edge if there is a significant co-expression relationship between them. Having gene expression profiles of a number of genes for several samples or experimental conditions, a gene co-expression network can be constructed by looking for pairs of genes which show a similar expression pattern across samples, since the transcript levels of two co-expressed genes rise and fall together across samples. Gene co-expression networks are of biological interest since co- expressed genes are controlled by the same transcriptional regulatory program, functionally related, or members of the same pathway or protein complex. The direction and type of co-expression relationships are not determined in gene co-expression networks; whereas in a gene regulatory network (GRN) a directed edge connects two genes, representing a biochemical process such as a reaction, transformation, interaction, activation or inhibition.
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