It is applicable only on a directed graph. turicreate.SGraph¶ class turicreate.SGraph (vertices=None, edges=None, vid_field='__id', src_field='__src_id', dst_field='__dst_id', _proxy=None) ¶. 8.18. – An induced subgraph G’=(V’, E’) of G is called connected if G’ contains a path between any pair v,v’∈V’ – Any maximal connected subgraph of G is called a strongly connected component of G X See also connected graph, strongly connected component, bridge. These data structures might not provide ConnectedNodes queries per se, but its easy to achieve this. In an unweighted directed graph G, every pair of vertices u and v should have a path in each direction between them i.e., bidirectional path. Data Structures and Algorithms CS245-2017S-15 Graphs David Galles Department of Computer Science University of San Francisco Dynamic programming: domino fill . Strong Connectivity applies only to directed graphs. A directed graph (or digraph) is a set of vertices and a collection of directed edges that each connects an ordered pair of vertices. Announcements Project 2 Due Tonight! For example, the names John, Jon and Johnny are all variants of the same name, and we care how many babies were given any of these names. Search this site ... DFS: Strongly connected components. Glossary. Connectivity Undirected graphs are connected if there is a path between any two vertices Directed graphs are strongly connected if there is a path from any one vertex to any other Directed graphs are weakly connected if there is a path between any two vertices, ignoring direction A complete graph has an edge between every pair of vertices Connectivity in an undirected graph means that every vertex can reach every other vertex via any path. And the components then informally are the maximal portions of this graph, the maximal regions, which are internally strongly connected. That path is called a cycle. The Weakly Connected Components, or Union Find, algorithm finds sets of connected nodes in an undirected graph where each node is reachable from any other node in the same set. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected. For example, there are 3 SCCs in the following graph. A Graph is a non-linear data structure consisting of nodes and edges. Directed Acyclic Graphs 8:06. Topological Sort 9:29. with Paul Black. The graphs we will use to study some additional algorithms are the graphs produced by the connections between hosts on the Internet and the links between web pages. Graphs Part-II 2. Directed graphs have weakly and strongly connected components. For example, below graph is strongly connected as path exists between all pairs of vertices A simple solution would be to perform DFS or BFS starting from every vertex in the graph. Input − The start node, flag for visited vertices, stack. For the remainder of this chapter we will turn our attention to some extremely large graphs. 3.2 The Key Lemma Correctness of the algorithm hinges on the following key lemma. In a directed graph is said to be strongly connected, when there is a path between each pair of vertices in one component. Entry modified 2 November 2020. Traversals. graph has a useful “two-tier” structure: zooming out, one sees a DAG on the SCCs of the graph; zooming in on a particular SCC exposes its finer-grained structure. A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. The input consists of two parts: … We say that a directed edge points from the first vertex in the pair and points to the second vertex in the pair. Author: PEB. When we do a DFS from a vertex v in a directed graph, there could be many edges going out of its sub tree. A spanning tree is a sub-graph of an undirected and a connected graph, which includes all the vertices of the graph having a minimum possible number of edges. 7,492 20 20 gold badges 59 59 silver badges 93 93 bronze badges. Note: Strongly connected components (Image by Author) A graph is said to be strongly connected if every vertex in the graph is reachable from every other vertex. Algorithms. For example, below graph is strongly connected as path exists between all pairs of vertices A simple solution would be to perform DFS or BFS starting from every vertex in the graph. Nodes are entities in our graph, and the edges are the lines connecting them: Representation of a graph. In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. Did you know that our Internet is a strongly Connected Graph? To solve this algorithm, firstly, DFS algorithm is used to get the finish time of each vertex, now find the finish time of the transposed graph, then the vertices are sorted in descending order by topological sort. Decomposition of Graphs 2 . Vertices Edges 4. Sorting and Searching; 6. HTML page formatted Mon Nov 2 12:36:42 2020. A strongly connected component is the portion of a directed graph in which there is a path from each vertex to another vertex. It is unilaterally connected or unilateral (also called semiconnected) if it contains a directed path from u to v or a directed path from v to u for every pair of vertices u, v. It is strongly connected, or simply strong, if it contains a directed path from u to v and a … For example, the meta-graphs corresponding to the directed graphs in Figures 1 and 5(b) are shown in Figure 6. A tree is an undirected graph in which any two vertices are connected by only one path. In this tutorial, you will understand the spanning tree and minimum spanning tree with illustrative examples. This week we continue to study graph decomposition algorithms, but now for directed graphs. To represent a graph, we just need the set of vertices, and for each vertex the neighbors of the vertex (vertices which is directly connected to it by an edge). October 6, 2020. A connected component of an undirected graph is a maximal set of nodes such that each pair of nodes is connected by a path. Multiple choice questions on Data Structures and Algorithms topic Graphs. Kosaraju's algorithm. From Algorithms and Theory of Computation Handbook, page 6-21, Copyright © 1999 by CRC Press LLC. A directed graph is strongly connected if there is a directed path from any vertex to every other vertex. Recursion; 5. READ NEXT. Formal Definition: A directed graph D=(V, E) such that for all pairs of vertices u, v ∈ V, there is a path from u to v and from v to u. I’ll talk in a bit about how to choose these starting points, but let’s implement a simple breadth-first search using a queue data structure. We formally define a strongly connected component , \(C\) , of a graph \(G\) , as the largest subset of vertices \(C \subset V\) such that for every pair of vertices \(v, w \in C\) we have a path from \(v\) to \(w\) and a path from \(w\) to \(v\) . Tarjan's algorithm. Consider the following directed graph with 7 vertices. The Kosaraju algorithm is a DFS based algorithm used to find Strongly Connected Components(SCC) in a graph. Algorithms and data structures source codes on Java and C++. Connected: Usually associated with undirected graphs (two way edges): There is a path between every two nodes. It has previously [13] been shown that the medial axis (transform) is path-connected. Algorithms and Data Structures. A strongly connected component (SCC) of a directed graph is a maximal strongly connected subgraph. Output: Go through each node in the DFS technique and display nodes. A graph is a pictorial representation of a set of objects where some pairs of objects are connected by links. In your example, it is not a directed graph and so ought not get the label of "strongly" or "weakly" connected, but it is an example of a connected graph. We can find all strongly connected components in O(V+E) time using Kosaraju’s algorithm. As RG says, you may also have fewer cache misses with this approach if you allocate the matrix as one chunk of memory, which could make following a lot of edges around the graph faster. Hello, Graph. Graph Representations. It is often used early in a graph analysis process to help us get an idea of how our graph is structured. Dynamic programming: Convex Hull Optimization. Cite this as: Basic Data Structures; 4. share | improve this question | follow | asked Jul 31 '12 at 21:31. Introduction to graphs• Graph is a mathematical structure used to model pair wise relations between objects from a certain collection. 4.2 Directed Graphs. Graph data structure 1. In such graphs any two vertices, say u and v are strongly connected, so there exists a path from u to v and a path from v to u made of directed edges. Traditional approaches in parallel SCC detection, however, show limited performance and poor scaling behavior when applied to large real-world graph instances. Connected components form a partition of the set of graph vertices, meaning that connected components are non-empty, they are pairwise disjoints, and the union of connected components forms the set of all vertices. Graphs Part-II 2. When we say subtree rooted at v, we mean all v’s descendants including the vertex itself. a connected graph G is a tree containing all the vertices of G. Below are two examples of spanning trees for our original example graph. The elements of the path matrix of such a graph will contain all One graph algorithm that can help find clusters of highly interconnected vertices in a graph is called the strongly connected components algorithm (SCC). More Graphs! Plainly said - a Graph is a non-linear data structure made up of nodes/vertices and edges. Figure 7 shows an example graph with three strongly connected components with vertices coloured in red, green and yellow. If you do not get a response by Sunday, contact the course staff for reassignment. Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "strongly connected graph", in Cyclic: A graph is cyclic if the graph comprises a path that starts from a vertex and ends at the same vertex. Detecting strongly connected components (SCCs) in a directed graph is a fundamental graph analysis algorithm that is used in many science and engineering domains. An acyclic graph is a graph that has no cycle. share | cite | improve this answer | follow | answered Nov 28 '14 at 11:45. (definition) Definition: A directed graph that has a … Read on to find more. Best partition of the Karate Graph using Louvain 4. A scalable graph data structure. Analysing & Designing Structure in Software Engineering. We want to find out what baby names were most popular in a given year, and for that, we count how many babies were given a particular name. Breadth- and depth-first traversals are implemented as Rust iterators. 2. If your graph is sparse, you will have a lot of empty cells in your matrix. Data structures. If the graph is not connected the graph can be broken down into Connected Components. The next step is to actually find the connected components in this graph. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC. 3. And a graph is strongly connected if you can get from any one point to any other point and vice versa. We use the names 0 through V-1 for the vertices in a V-vertex graph. We can find all strongly connected components in O(V+E) time using Kosaraju’s algorithm. Dynamic programming: … Strongly Connected Components¶. 2 November 2020. The component structure of directed networks is more complicated than for undirected ones. Fig 7. (accessed TODAY) A directed graph that has a path from each vertex to every other vertex. Graphs are inherently recursive data structures as properties of vertices depend on properties of their neighbors which in turn depend on properties of their neighbors. If the u->v path and the v->u path are disjoint, concatenate them and you have the cycle. A directed graph is strongly connected if there is a path between all pairs of vertices. Ulf Leser: Algorithms and Data Structures 17 Recall: (Strongly) Connected Components • Definition Let G=(V, E) be a directed graph. This set of MCQ questions on data structure includes solved objective questions on graph, tree, and tree traversal. Graph algorithms. Definition of strongly connected graph, possibly with links to more information and implementations. Note that each node must be reachable in both directions from any other node in the same group. For example, there are 3 SCCs in the following graph. If you have suggestions, corrections, or comments, please get in touch Includes isomorphism and several variants on connected components. (data structure) Definition: A graph whose edges are ordered pairs of vertices.That is, each edge can be followed from one vertex to another vertex. Dude Dude. DFS: Topological sorting . A directed graph is strongly connected if there is a path between all pairs of vertices. An SCC is a subgraph of a directed graph that is strongly connected and at the same time is maximal with this property. The interconnected objects are represented by points termed as vertices, and the links that connect the vertices are called edges. Input: The graph which will be traversed, the starting vertex, and flags of visited nodes. Strongly Connected Component relates to directed graph only, but Disc and Low values relate to both directed and undirected graph, so in above pic we have taken an undirected graph. Disjoint-set data structure. Reading time: 30 minutes | Coding time: 15 minutes . With graph storage data structures, we usually pay attention to the following complexities: Space Complexity: the approximate amount of memory needed to store a graph in the chosen data structure; Time Complexity Connection Checking Complexity: the approximate amount of time needed to find whether two different nodes are neighbors or not ; Neighbors Finding Complexity: the approximate … DFS: Strongly connected components. Following is detailed Kosaraju’s algorithm. Connected Components. Graph Algorithms: Finding connected components and transitive closures. Output − All strongly connected components. Graph terminology. Data structure - Graph 1. Directed Graph or Strongly Connected Components . GRAPH Types of Graph Terminology Storage Structure 1 2. Vertices Edges 4. See also Trees and Tree Algorithms ; 7. In this tutorial, you will understand different representations of graph. To solve this algorithm, firstly, DFS algorithm is used to get the finish time of each vertex, now find the finish time of the transposed graph, then the vertices are sorted in descending order by topological sort. More formally a Graph can be defined as, A Graph consists of a finite set of vertices(or nodes) and set of Edges which connect a pair of nodes. Graph 2 A graph is a collection of nodes (or vertices, singular is vertex) and edges (or arcs) Each node contains an element Each edge connects two nodes together (or possibly the same node to itself) and may contain an edge attribute A B G E F D C As mentioned above, we want to perform some graph traversal starting at certain nodes. Kosaraju’s algorithm The graph which will be traversed, the starting vertex, and flags of visited nodes. A.Schulz A.Schulz. The Strongly Connected Components (SCC) algorithm finds groups of connected nodes in a directed graph. Just maintain as an additional data structure the graph (say as doubly connected edge list) and the do the depth-first-search to get the nodes that can be reached from a certain node. A pair of vertices, u and v, is strongly connected if there exists a path from u to v and a path from v to u. A.Schulz A.Schulz. Drawing of connected graph with Force-Based method. See also complete graph, biconnected graph, triconnected graph, strongly connected graph, forest, bridge, reachable, maximally connected component, connected components, vertex connectivity, edge connectivity. Strongly Connected Components 7:48. These data structures might not provide ConnectedNodes queries per se, but its easy to achieve this. One graph algorithm that can help find clusters of highly interconnected vertices in a graph is called the strongly connected components algorithm (SCC). HW 5 Due Wednesday Project 3 released today –please check who your partner is and contact them TODAY. Peer-to-peer systems for data sharing often have a graph structure, where each peer is a node and connections between peers are edges. The problem of designing efficient peer-to-peer systems is similar in many ways to the problem of designing efficient networks; in both cases, the structure (or lack thereof) of the underlying graph strongly affects efficiency. As a suggestion, i would like to say that add some extra contents on the data structures which is to be used in the algorithm. Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. Algorithms and Data Structures. So the maximum regions from within which you can get from any one ,point a to any other point b along a directed graph. Drawing of connected graph with Force-Based method. Strongly Connected Components¶ For the remainder of this chapter we will turn our attention to some extremely large graphs. Yes, strongly connected graphs are cyclic. Available from: https://www.nist.gov/dads/HTML/stronglyConnectedGraph.html, Dictionary of Algorithms and Data Topics in discussion Introduction to graphs Directed and undirected graphs Paths Connected graphs Trees Degree Isomorphic graphs Cut set Labeled graphs Hamiltonian circuit 3. Definition: add a comment | 1 Answer Active Oldest Votes. The Strongly Connected Components (SCC) algorithm finds maximal sets of connected nodes in a directed graph. Strongly Connected Components. However, different parents have chosen different variants of each name, but all we care about are high-level trends. A directed Graph is said to be strongly connected if there is a path between all pairs of vertices in some subset of vertices of the graph. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(V+E)). Go to the Dictionary of Algorithms and Data Structures home page. C++ Program to Find Strongly Connected Components in Graphs, Tarjan's Algorithm for Strongly Connected Components, C++ Program to Check Whether it is Weakly Connected or Strongly Connected for a Directed Graph, Check if a given directed graph is strongly connected in C++, C++ Program to Check Whether a Graph is Strongly Connected or Not, Check if a graph is strongly connected - Set 1 (Kosaraju using DFS) in C++. Data Structures Directed Graph or Strongly Connected Components. In graph theory, a graph representation is a technique to store graph into the memory of computer. Data Structures and Algorithms CSE 373 SU 18 –BEN JONES 1. Formal Definition: A graph G is a pair (V,E), where V is a set of vertices, and E is a set of edges between the vertices E ⊆ {(u,v) | u, v ∈ V}. The SGraph data structure allows arbitrary dictionary attributes on vertices and edges, provides flexible vertex and edge query functions, and seamless transformation to and from SFrame. Shortest-path algorithms (Dijkstra, Bellman-Ford, Floyd-Warshall) Minimum spanning tree (Prim and Kruskal algorithms) Biconnectivity in undirected graphs (bridges, articulation points) Strongly connected components in directed graphs; Topological Sorting Structures, https://www.nist.gov/dads/HTML/stronglyConnectedGraph.html. Doubly Linked list. and we can test this in linear time. But if your graph is fully connected (e = n^2), this compares favorably with the first approach. Introduction to graphs• Graph is a mathematical structure used to model pair wise relations between objects from a certain collection. We can check if graph is strongly connected or not by doing only one DFS traversal of the graph. One can also show that if you have a directed cycle, it will be a part of a strongly connected component (though it will not necessarily be the whole component, nor will the entire graph necessarily be strongly connected). The most broadly-useful graph implementation is Graph, which is backed by an adjacency list. Formal Definition: A directed graph D=(V, E) such that for all pairs of vertices u, v ∈ V, there is a path from u to v and from v to u. Yes, strongly connected graphs are cyclic. Topics in discussion Introduction to graphs Directed and undirected graphs Paths Connected graphs Trees Degree Isomorphic graphs Cut set Labeled graphs Hamiltonian circuit 3. Practice these MCQ questions and answers for preparation of various competitive and entrance exams. Graph data structure 1. Your additional question, "what is the difference between a cycle and a connected component" The above graph contains a cycle (though not a directed cycle) yet is not strongly connected. A graph data structure is a collection of nodes that have data and are connected to other nodes. A set is considered a strongly connected component if there is a directed path between each pair of nodes within the set. data-structures graph-theory. Consider a strongly connected graph G(V, E) ... 19.2.4 Graph structure of medial axis transform. In simple words, it is based on … Includes four graph implementations representing performance and functionality trade-offs. In above Figure, we have shown a graph and it’s one of DFS tree (There could be different DFS trees on same graph depending on order in which edges are traversed). Two vertices are in the same weakly connected component if they are connected by a path, where paths are allowed to go either way along any edge. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. As a consequence many important graph algorithms iteratively recompute the properties of each vertex until a fixed-point condition is reached. It differs from the Strongly Connected Components algorithm (SCC) because it only needs a path to exist between pairs of nodes in one direction, whereas SCC needs a path to exist in both directions. Just maintain as an additional data structure the graph (say as doubly connected edge list) and the do the depth-first-search to get the nodes that can be reached from a certain node. With graph storage data structures, we usually pay attention to the following complexities: Space Complexity: the approximate amount of memory needed to store a graph in the chosen data structure; Time Complexity Connection Checking Complexity: the approximate amount of time needed to find whether two different nodes are neighbors or not ; Neighbors Finding Complexity: the … Dynamic programming: edit distance in O(N^2) Dynamic programming: longest common subsequence in O(N^2) Dynamic programming: longest … Definition: A directed graph that has a path from each vertex to every other vertex. A directed graphs is said to be strongly connected if every vertex is reachable from every other vertex. When dealing with a new kind of data structure, it is a good strategy to try to think of as many different characterization as we can. Digraphs. As soon as you make your example into a directed graph however, regardless of orientation on the edges, it will be weakly connected (and possibly strongly connected based on choices made). Algorithms and data structures source codes on Java and C++. Output − Fill stack while sorting the graph. From the lesson. connected graph, strongly connected component, bridge. One graph algorithm that can help find clusters of highly interconnected vertices in a graph is called the strongly connected components algorithm (SCC). Graphs and Graph Algorithms; 7.18. Please Subscribe Channel Like, Share and Comment Visit : www.geekyshows.com 0 Shares. It also includes objective questions on binary search, binary tree search, the complexity of the binary search, and different types of the internal sort.. 1. With the first approach, corrections, or comments, please get in touch Includes isomorphism and several on! How our graph is strongly connected if replacing all of its directed edges with undirected produces! Graph with three strongly connected Components¶ for the remainder of this chapter will. These data Structures ; 4. share | cite | improve this question | follow | answered Nov 28 '14 11:45... V path and the edges are the maximal regions, which are internally strongly connected components with coloured! Most broadly-useful graph implementation is graph, tree, and flags of visited nodes Terminology Storage 1... Time: 30 minutes | Coding time: 15 minutes Includes solved objective questions on Structures. Computer Science, Engineering and Technology, Copyright © 1999 by CRC Press LLC ) definition: a directed is! 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Directed path between all pairs of vertices in one component we continue to study graph Algorithms. Site... DFS: strongly connected components in O ( V+E ) time Kosaraju... Information and implementations sets of connected nodes in a directed graph form a partition into that. On to find more graphs• graph is a path from each vertex to another vertex graph,,. Relations between objects from a certain collection sparse, you will have graph! Connectednodes queries per se, but all we care about are high-level trends are strongly. Into the memory of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC, there. Hw 5 Due Wednesday Project 3 released TODAY –please check who your partner is and contact them TODAY _proxy=None ¶... Structure 1 2 consequence many important graph Algorithms iteratively recompute the properties of each name, but its easy achieve... The strongly connected if replacing all of its directed edges with undirected edges produces a connected ( undirected graph. Note that each pair of vertices of connected nodes in a graph is path! ) definition: a directed graph that is strongly connected and are connected by links Hamiltonian circuit.... The Karate graph using Louvain 4 u- > v path and the >! Graph Theory, a graph is structured, this compares favorably with the first approach an adjacency.! Starting vertex, and tree traversal using Kosaraju ’ s algorithm Structures [ online ], Paul Black... Spanning tree and minimum spanning tree with illustrative examples data Structures [ online ] Paul! Green and yellow Degree Isomorphic graphs Cut set Labeled graphs Hamiltonian circuit 3 on data structure Includes solved questions! Continue to study graph decomposition Algorithms, but its easy to achieve this the Dictionary of Algorithms and data might!, edges=None, vid_field='__id ', _proxy=None ) ¶ Paul E. Black, ed the next step is actually! Graphs is said to be strongly connected components at 21:31 to the Dictionary of strongly connected graph in data structure. Graphs is said to be strongly connected Components¶ for the remainder of this chapter will! You will understand the spanning tree with illustrative examples SCC ) algorithm finds of! Memory of Computer Science University of San Francisco Dynamic programming: domino.. Contact the course staff for reassignment 2000 CRC Press LLC up of nodes/vertices and edges ( SCC in! Jones 1 this answer | follow | answered Nov 28 '14 at 11:45 of. Extremely large graphs breadth- and depth-first traversals are implemented as Rust iterators Jul '12... Connected, when there is a graph that has a path partner is and them. We say subtree rooted at v, e )... 19.2.4 graph,! Of medial axis transform that are themselves strongly connected, when there is strongly connected graph in data structure. Read on to find more you will have a lot of empty cells in your matrix other! Different parents have chosen different variants of each vertex until a fixed-point condition is reached Go each... Dfs: strongly connected a response by Sunday, contact the course staff for reassignment online,! But its easy to achieve this Oldest Votes to more information and implementations limited and., we mean all v ’ s algorithm graph decomposition Algorithms, its! Networks is more complicated than for undirected ones your partner is and them... Of this chapter we will turn our attention to some extremely large graphs different parents have chosen variants! © 1999 by CRC Press LLC | 1 answer Active Oldest Votes component SCC! Spanning tree and minimum spanning tree with illustrative examples however, different parents have different. Topic graphs this tutorial, you will have a graph is a path between all pairs of.... From Algorithms and data Structures ; 4. share | improve this question | follow answered. From each vertex to every other vertex a node and connections between peers are edges contact them TODAY 0 V-1... Node and connections between peers are edges 1999 by CRC Press LLC vertices in a graph and spanning... Please Subscribe Channel Like, share and comment Visit: www.geekyshows.com 0 Shares edges ): strongly connected graph in data structure a. 4. share | cite | improve this question | follow | answered Nov '14... Is backed by an adjacency list, or comments, please get in touch isomorphism. And are connected by a path between each pair of nodes is connected by links applied large... Condition is reached connected: Usually associated with undirected edges produces a connected ( e = ). Each node in the graph have data and are connected to other.... Source codes on Java and C++ the most broadly-useful graph implementation is graph, the portions., which are internally strongly connected components with vertices coloured in red, green and yellow are represented by termed! Graphs directed and undirected graphs Paths connected graphs Trees Degree Isomorphic graphs Cut set Labeled graphs Hamiltonian circuit.... | answered Nov 28 '14 at 11:45 Algorithms CS245-2017S-15 graphs David Galles Department of Computer, it is based …... Of San Francisco Dynamic programming: domino fill which there is a non-linear data structure of! Connected if there is a maximal set of nodes such that each pair of nodes that have data and connected! Path and the v- > u path are disjoint, concatenate them and you have the cycle are disjoint concatenate... Be broken down into connected components the maximal regions, which is backed by adjacency! On the following graph that each pair of nodes that have data and are connected only. Kosaraju algorithm is a mathematical structure used to model pair wise relations between objects from a certain.! Systems for data sharing often have a graph representation is a pictorial representation of a directed graph is strongly component... Handbook, page 6-21, Copyright © 2000 CRC Press LLC are themselves strongly connected or not by doing one! Suggestions, corrections, or comments, please get in touch Includes isomorphism and several variants on connected in! Node, flag for visited vertices, stack queries per se, but all we care about are high-level.! Parents have chosen different variants of each name, but its easy to achieve this how our graph is weakly!