A strongly connected component is the portion of a directed graph in which there is a path from each vertex to another vertex. Everything else will be used for testing. Transforming your data into StellarGraph is really simple, you just provide the node features and edges dataframes to the StellarGraph function. STEP 2: Replace all the diagonal elements with the degree of nodes. Algorithm to Reverse the Graph. Node 3 is connected to: 2. Graph (adjacency_dict) # create a Graph dict mapping nodes to nbrs >>> list (H. edges ()) to_directed (graph) Returns a directed view of the graph graph. Node 1 is connected to: 2 0 As you can see from the information printed, weve read in our data correctly. Claim Your Discount. I will show you then how to apply this model to the real-world dataset. Topological sort (acyclic graph, adjacency matrix) - O(V 2) Traveling Salesman Problem (brute force) - O(n!) Traveling Salesman Problem (dynamic programming, iterative) - O(n 2 2 n ) For a directed graph the only change would be that the linked list will only contain the node on which the incident edge is present. How to find if a given edge is a bridge? Data Structures & Algorithms- Self Paced Course, Traversal of a Graph in lexicographical order using BFS, Detect Cycle in a Directed Graph using BFS, Detect cycle in an undirected graph using BFS, Check if a given directed graph is strongly connected | Set 2 (Kosaraju using BFS), Print the lexicographically smallest BFS of the graph starting from 1. One way to do this is with adjacency lists which is a method of storing our graph in memory by associating each node with its neighbors and the cost of the edge between them. You might have noticed that if we remove the non-trainable part, were left with simple dense layer. Follow edges one at a time. Since were working with neural networks we need to one-hot-encode the labels. Therefore overall time complexity is O((V+E)*(V+E)) which can be written as O(E2) for a connected graph. Time Complexity : O(V+E) where V is the number of vertices in graph and E is the number of edges in graphAuxiliary Space: O(V)Please refer complete article on Depth First Search or DFS for a Graph for more details! Let us say we pick 2-0. Three edges are going out from vertex 2, which one to pick? Creating Directed Graphs using the NetworkX Package. The C++ implementation uses adjacency list representation of graphs. Theres a couple more formalities we need to take care of before modelling: Now that data is normalised and in the right shape, we can move to modelling. Kosaraju's Algorithm is based on the depth-first search algorithm implemented twice. In this section, we will learn Java Graph data structure in detail. Once an edge is processed (included in the Euler tour), we remove it from the graph. Given a boolean 2D matrix, find the number of islands. The idea is to store the complete path between the source and destination vertex in an array using recursion. Approach: Take two bool arrays vis1 and vis2 of size N (number of nodes of a graph) and keep false in all indexes. The idea is to start the BFS routine from the source vertex and check if the destination vertex is reached during the traversal. Interactive Courses, where you Learn by writing Code. Perform depth-first search on the reversed graph. First of all, lets initialise the Input layers with the correct shapes to receive our 3 inputs: Now, we can build a model with 2 GCN dropout layers. Adjacency Matrix 2. When we come to vertex 0, we look for all adjacent vertices of it. The first thing you need to know to construct an adjacency list is the number of nodes in a graph. These components can be found using Kosaraju's Algorithm. In the above-mentioned post, we discussed the problem of finding out whether a given graph is Eulerian or not. 2. Program to print prime numbers from 1 to N. Python program to print all Prime numbers in an Interval, Python program to check whether a number is Prime or not. As you can see, there are 2 parts of this equation - non-trainable (with D, A) and trainable (with H, A). Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Adjacency List There are other representations also like, Incidence Matrix and Incidence List. GCN is a semi-supervised model meaning that it needs significantly less labels than purely supervised models (e.g. As you could guess from the name, GCN is a neural network architecture that works with graph data. So, lets imaging the we have only 1% of data labeled which is about 400 developers. 1 0 1 0 Consider the graph shown below: The above graph is a directed one and the Adjacency list for this looks like: Implementation of Adjacency List. If you use the stellargraph API fully (example below) the training process will be a lot faster. A graph where all vertices are connected with each other has exactly one connected component, consisting of the whole graph. Practice SQL Query in browser with sample Dataset. More formally, the Graph Convolutional Layer can be expressed using this equation: Here, for every vertex in the graph, we have a list of all the other vertices which the particular vertex has an edge to. We keep track of the visited 1s so that they are not visited again. Articulation Points (or Cut Vertices) in a Graph; Bridges in a graph; Eulerian path and circuit for undirected graph; Fleurys Algorithm for printing Eulerian Path or Circuit; Hierholzers Algorithm for directed graph; Euler Circuit in a Directed Graph; Find if an array of strings can be chained to form a circle | Set 1 In the binary classification problem (like ours) we dont actually have to do this, since we can just use sigmoid activation function at the final layer. Run This Code Code: import java. Time Complexity: The time complexity of the above implementation is O ((V+E)2). By default these methods create a DiGraph/Graph class and you probably want them to create your extension of a DiGraph/Graph. Time Complexity : O(ROW * COL) where ROW is number of ROWS and COL is number of COLUMNS in the matrix. If a path exists from the source vertex to the destination vertex, print it. In degree is equal to the out degree for every vertex. This website uses cookies. Exercise: Extend the solution to print all paths between given vertices (solution link). The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again. A graph where all vertices are connected with each other has exactly one connected component, consisting of the whole graph. Such graph with only one connected component is called as Strongly Connected Graph.We have discussed a DFS solution for islands is already discussed. To make these experiments faster and less complicated, lets now use the StellarGraph API fully. Now, we can train the model in the same way we did before. See this post for all applications of Depth First Traversal.Following are implementations of simple Depth First Traversal. To remove the edge, we replace the vertex entry with -1 in the adjacency list. We are sorry that this post was not useful for you! The longest path problem for a general graph is not as easy as the shortest path problem because the longest path problem doesnt have optimal substructure property.In fact, the Longest Path problem is NP-Hard for a The graph shown above is an undirected one and the adjacency matrix for the same looks as: The above matrix is the adjacency matrix representation of the graph shown above. To facilitate this we define two class variables that you can set in your subclass. 0-1 BFS (Shortest Path in a Binary Weight Graph). The main goal of GCN is to distill graph and node attribute information into the vector node representation aka embeddings. Since we know now what happens under the hood, lets simply import the layer and use it in our architecture. We can use the Breadthfirst search (BFS) algorithm to check the connectivity between any two vertices in the graph efficiently. 2 is also an adjacent vertex of 0. Hence, by multiplying the hidden state (or node features in the first layer) by it, we are sort of applying a mask and aggregating only the information from neighbouring nodes. Following is the C++ implementation of the above algorithm. The complexity is O (NE) where N is the number of vertices and E is the number of the edges for each vertex. The final question to answer is - why do we need to normalise the adjacency matrix? Count all possible Paths between two Vertices, Detect a negative cycle in a Graph | (Bellman Ford), Cycles of length n in an undirected and connected graph, Detecting negative cycle using Floyd Warshall, Detect Cycle in a directed graph using colors, Introduction to Disjoint Set Data Structure or Union-Find Algorithm, Union By Rank and Path Compression in Union-Find Algorithm, Fleurys Algorithm for printing Eulerian Path or Circuit, Johnsons algorithm for All-pairs shortest paths, Comparison of Dijkstras and FloydWarshall algorithms, Find minimum weight cycle in an undirected graph, Find Shortest distance from a guard in a Bank, Maximum edges that can be added to DAG so that it remains DAG, Given a sorted dictionary of an alien language, find order of characters, Find the ordering of tasks from given dependencies, Topological Sort of a graph using departure time of vertex, Prims Minimum Spanning Tree (MST) | Greedy Algo-5, Applications of Minimum Spanning Tree Problem, Total number of Spanning Trees in a Graph, Check if a graph is strongly connected | Set 1 (Kosaraju using DFS), Tarjans Algorithm to find Strongly Connected Components, Articulation Points (or Cut Vertices) in a Graph, Dynamic Connectivity | Set 1 (Incremental), Ford-Fulkerson Algorithm for Maximum Flow Problem, Push Relabel Algorithm | Set 1 (Introduction and Illustration), Graph Coloring | Set 1 (Introduction and Applications), Traveling Salesman Problem (TSP) Implementation, Travelling Salesman Problem using Dynamic Programming, Approximate solution for Travelling Salesman Problem using MST, Introduction and Approximate Solution for Vertex Cover Problem, Chinese Postman or Route Inspection | Set 1 (introduction), Hierholzers Algorithm for directed graph, Number of Triangles in an Undirected Graph, Construct a graph from given degrees of all vertices, https://www.geeksforgeeks.org/eulerian-path-and-circuit/, Hierholzer's Algorithm for directed graph. So, unlike standard BFS(), where we process all adjacent vertices, we process 8 neighbours only. Path exists from vertex 0 to vertex 7. Vote count: 165. Adjacency Matrix; Adjacency List; Edge List; Adjacency Matrix. MCQs to test your C++ language knowledge. We remove edge u-v and again count the number of reachable vertices from u. We could also use a hash map where the keys represent the node and the values are the lists of neighbors. Path exists from vertex 0 to vertex 7 To understand what kind of pre-processing we need to do, lets take a look at what the Graph Convolutional Layer will be doing. Now the only thing left is to print the graph. As you can see, two classes are quite distinctly clustered in the opposite sides of the graph. I hope that by now you know not only how to apply GCNs to your data but also feel more confident about whats happening under the hood. H^{(l+1)} = \sigma(\tilde{D}^{-1/2}\tilde{A}\tilde{D}^{-1/2}{H^{(l)}}{W^{(l)}}) The concept of the graph has been stolen from the mathematics that fulfills the need of the computer science field. A strongly connected component is the portion of a directed graph in which there is a path from each vertex to another vertex. Graph Implementation in Python. We can detect singly connected component using Kosarajus DFS based simple algorithm. ; Make all visited vertices v as vis1[v] = true. Path exists from vertex 0 to vertex 7 We can also do DFS V times starting from every vertex. Time Complexity : O(V*V) as adjacency matrix is used for graph but can be made O(V+E) by using adjacency list. The choice of graph representation is situation-specific. For the directed graph shown above the adjacency matrix will look something like this: The structure (constructor in Java) for the adjacency matrix will look something like this: It should also be noted that we have two class-level variables, like: We have a constructor above named AdjacencyMatrix which takes the count of the number of the vertices that are present in the graph and then assigns our global vertex variable that value and also creates a 2D matrix of the same size. We will store our list in a python dictionary. Now since our structure part is complete, we are simply left with adding the edges together, and the way we do that is: In the above addEdge function we also assigned 1 for the direction from the destination to the start node, as in this code we looked at the example of the undirected graph, in which the relationship is a two-way process. Since you understand whats happening under the hood, theres nothing wrong with making your life easier! Given an undirected or a directed graph, implement a graph data structure in C++ using STL. Note that simply deleting the node may not work as the code is recursive and a parent call may be in the middle of the adjacency list. In contrast, there is no path from vertex 7 to any other vertex. Space Complexity : O(V) due to queue and color vector. 0 0 1 0. A directed graph has an eulerian cycle if following conditions are true. This part is key for GCNs to work. Output Adjacency list of vertex 0 : 1 2 6 Adjacency list of vertex 1 : 2 Adjacency list of vertex 2 : 6 Adjacency list of vertex 3 : 2 Adjacency list of vertex 4 : 3 5 Adjacency list of vertex 5 : 1 Adjacency list of vertex 6 : 5 Path is exist between (5-2) Path is not exist between (0-4) Last updated on June 21, 2021 by Kalkicode element with the index 1represents a node 1. in C language implement a graph coloring method that assigns the minimum color to each vertex so it does conflict with vertices that have been colored (using adjacency list) arrow_forward I have a directed graph with N nodes. If there are zero odd vertices, we start from vertex 0. For directed graphs, only outgoing adjacencies are included. We learned how to represent the graphs in programming, via adjacency matrix and adjacency lists. Implementation of a directed and weighted graph, with graph algorithms. The alternative is to use the idea of information passing by multiplying the hidden state by the adjacency matrix. A connected component of an undirected graph is a subgraph in which every two vertices are connected to each other by a path(s), and which is connected to no other vertices outside the subgraph. No votes so far! # python 3 program for # show degree of vertex in directed graph class ajlistnode : # vertices node key def __init__ (self, id) : # set value of node key self.id = id self.next = none class vertices : def __init__ (self, data) : self.data = data self.next = none self.last = none class graph : # number of vertices def 0 1 0 1 to_directed_class callable, (default: DiGraph or MultiDiGraph) Class to create a new graph structure in the to_directed method. The complete path is 0 3 4 6 7, Output: It represents a network that connects multiple points to each other. Read our, // a vector of vectors to represent an adjacency list in C++, // resize the vector to hold `n` elements each of type `vector
`, // Function to perform BFS traversal from a given source vertex in a graph to, // determine if a destination vertex is reachable from the source or not, // get the total number of nodes in the graph, // to keep track of whether a vertex is discovered or not, // vector of graph edges as per the above diagram, // total number of nodes in the graph (labeled from 0 to 7), // perform BFS traversal from the source vertex to check the connectivity, // Factory method for creating an immutable instance of `Edge`, // A list of lists to represent an adjacency list, // List of graph edges as per the above diagram, # A list of lists to represent an adjacency list, # Function to perform BFS traversal from a given source vertex in a graph to, # determine if a destination vertex is reachable from the source or not, # get the total number of nodes in the graph, # to keep track of whether a vertex is discovered or not, # List of graph edges as per the above diagram, # total number of nodes in the graph (labeled from 0 to 7), # perform BFS traversal from the source vertex to check the connectivity, 'Path exists from vertex {src} to vertex {dest}', 'No path exists between vertices {src} and {dest}', // resize the vector to hold `n` elements of type `vector`, // Function to perform DFS traversal in a directed graph to find the, // complete path between source and destination vertices, // return true if the destination is found, // backtrack: remove the current node from the path, // return false if destination vertex is not reachable from src, // vector to store the complete path between source and destination, // perform DFS traversal from the source vertex to check the connectivity, // and store path from the source vertex to the destination vertex, // To store the complete path between source and destination, # Function to perform DFS traversal in a directed graph to find the, # complete path between source and destination vertices, # return true if the destination is found, # backtrack: remove the current node from the path, # return false if destination vertex is not reachable from src, # List to store the complete path between source and destination, # perform DFS traversal from the source vertex to check the connectivity, # and store path from the source vertex to the destination vertex, Young Tableau | Insert, Search, Extract-Min, Delete, Replace. Also, we will learn the types of Graph, their Euler tour becomes 2-0 0-1 1-2, Again there is only one edge from vertex 2, so we pick it, remove it and move to vertex 3. The adjacency List representing the graph is: {0: [1, 3], 1: [0, 2, 3], 2: [4, 1, 5], 3: [4, 0, 1], 4: [2, 3, 5], 5: [4, 2], 6: []} BFS traversal of graph with source 0 is: 0-->1-->3-->2-->4-->5--> If you have not been able to understand the execution of the code, here is a If any DFS, doesnt visit all vertices, then graph is not strongly connected. In this post, an algorithm to print an Eulerian trail or circuit is discussed. STL\s list container is used to store lists of adjacent nodes. Try Programiz PRO: Complexity Analysis: Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph. If we look closely, we can see that the matrix is symmetric. classification, The time complexity of DFS for adjacency list representation is O(V+E). This is demonstrated below in C++, Java, and Python: Output: to_directed_class callable, (default: DiGraph or MultiDiGraph) Class to create a new graph structure in the to_directed method. You can see this in the implementation of stellargraphs GraphConvolution layer on github in lines 208 and 209. In each BFS() call, a component or a sub-graph is visited. If the destination vertex is not encountered at any point, we can say that its not reachable from the source vertex. If there are 2 odd vertices, start at one of them. By default these methods create a DiGraph/Graph class and you probably want them to create your extension of a DiGraph/Graph. Return false as the destination is not reached in BFS. G.edges: It returns the list of edges in the graph. The rest of the cells contains either 0 or 1 (can contain an associated weight w if it is a weighted graph). Add an edge to the graph To add an edge (u,v) to the graph, We will first check if both the edges u and v are present in Start DFS at the vertex which was chosen at step 2. It totally depends on the type of operations to be performed and ease of use. This data type also supports weighted edges, heterogeneous node and edge types, and directed graphs. Enter your email address to subscribe to new posts. First, lets pre-process our labels data. Eulerian Circuit is an Eulerian Path that starts and ends on the same vertex. The idea is, dont burn bridges so that we can come back to a vertex and traverse the remaining edges. Below you can see the intuitive depiction of GCN from Kipf and Welling (2016) paper. Java Graph. The main focus is to print an Eulerian trail or circuit. Now that we have the trained model, lets evaluate its accuracy on the test set weve set aside. Each vertex has its own linked-list that contains the nodes that it is connected to. G.adj: It returns the adjacency list for all the nodes. Since node 3 has edges to nodes 1 and 2, graph[3] has the adjacency list {1, 2}. The following two are the most commonly used representations of a graph. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. We traverse all adjacent vertices of u, if there is only one adjacent vertex, we immediately consider it. If youre not familiar with the Keras interface, I recommend checking their tutorials here. Traverse each adjacency list and while traversing keep adding the reverse edges (making source as destination and destination as source). We can use isEulerian() to first check whether there is an Eulerian Trail or Circuit in the given graph. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Fundamentals of Java Collection Framework, Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Find the number of Islands using Disjoint Set, Connected Components in an Undirected Graph, Check if a graph is strongly connected | Set 1 (Kosaraju using DFS), Tarjans Algorithm to find Strongly Connected Components, Articulation Points (or Cut Vertices) in a Graph, Eulerian path and circuit for undirected graph, Fleurys Algorithm for printing Eulerian Path or Circuit, Hierholzers Algorithm for directed graph, Find if an array of strings can be chained to form a circle | Set 1, Find if an array of strings can be chained to form a circle | Set 2, Kruskals Minimum Spanning Tree Algorithm | Greedy Algo-2, Prims Minimum Spanning Tree (MST) | Greedy Algo-5, Prims MST for Adjacency List Representation | Greedy Algo-6, Dijkstras Shortest Path Algorithm | Greedy Algo-7, Dijkstras Algorithm for Adjacency List Representation | Greedy Algo-8, Dijkstras shortest path algorithm using set in STL, Dijkstras Shortest Path Algorithm using priority_queue of STL, Dijkstras shortest path algorithm in Java using PriorityQueue. Note that the above code modifies the given graph, we can create a copy of the graph if we dont want the given graph to be modified. Depth First Traversal (or Search) for a graph is similar to Depth First Traversal of a tree. Were going to classify github users into web or ML developers. It is applicable only on a directed graph. While these methods were quite successful in representing the nodes, they could not incorporate node features into these embeddings. 8.5. Let us start the tour from vertex 2. The adjacency List representing the graph is: {0: [1, 3], 1: [0, 2, 3], 2: [4, 1, 5], 3: [4, 0, 1], 4: [2, 3, 5], 5: [4, 2]} The new vertices of the graph are: {0, 1, 2, 3, 4, 5, 6} 4. Ltd. The above graph is a directed one and the Adjacency list for this looks like: The structure (constructor in Java) for the adjacency list will look something like this: The above constructor takes the number of vertices as an argument and then assigns the class level variable this value, and then we create an array of LinkedList of the size of the vertices present in the graph. In Python, we can do this with a dictionary (other languages might use linked lists). When to use DFS or BFS to solve a Graph problem? The time complexity of DFS for adjacency list representation is O(V+E). Zak Jost has made a great video explaining these concepts in detail, so if youre a bit unclear about why we need to multiply by the adjacency matrix, make sure to check out his video. Adjacency List; Adjacency Matrix. Connected Components for undirected graph using DFS: Finding connected components for an undirected graph is an Space Complexity: O(V).Since an extra visited array is needed of size V. This algorithm aims to find the shortest-path in a directed or undirected graph with non-negative edge weights. We remove this edge and move to vertex 0. There is only one edge from vertex 0, so we pick it, remove it and move to vertex 1. Data Structures & Algorithms- Self Paced Course, Eulerian path and circuit for undirected graph, Java Program for Dijkstra's Algorithm with Path Printing, Printing Paths in Dijkstra's Shortest Path Algorithm, Conversion of an Undirected Graph to a Directed Euler Circuit, Java Program to Optimize Wire Length in Electrical Circuit, Program to find Circuit Rank of an Undirected Graph, Minimum edges required to add to make Euler Circuit, Shortest path from source to destination such that edge weights along path are alternatively increasing and decreasing. For example, the below matrix contains 5 islands, What is an island? Thank you for reading, and if you have any questions or comments, feel free to reach out using my email or LinkedIn. Lets go through the Adjacency List of the Graph and reverse the edges and store them in a new Adjacency List. An adjacency list is similar to an adjacency matrix in the fact that it is a way of representing a graph, however it uses linked lists to store the connections between nodes. graph = Graph(5, directed = False) 2.3 (Adjacency List) 2.3.1 . adjacency_list Graph. We first find the starting point which must be an odd vertex (if there are odd vertices) and store it in variable u. To count reachable vertices, we can either use BFS or DFS, we have used DFS in the above code. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. It works well with image data because the neighbours are ordered and fixed in size. The number of calls to BFS() gives the number of connected components. To facilitate this we define two class variables that you can set in your subclass. Given a directed graph and two vertices (say source and destination vertex), determine if the destination vertex is reachable from the source vertex or not. BFS can also be used. A Depth First Traversal of the following graph is 2, 0, 1, 3. Thus, the strongly connected components are. A most common way to create a graph is by using one of the representations of graphs like adjacency matrix or adjacency list. In a weighted graph, the element A[i][j] represents the cost of moving from vertex i to vertex j. Prerequisites: See this post for all applications of Depth First Traversal. This class is built on top of GraphBase, so the order of the methods in the generated API documentation is a little bit obscure: inherited methods come after the ones implemented directly in the subclass. A group of connected 1s forms an island. Graph Representations - Adjacency Matrix and List. C++ Java Python3 Parewa Labs Pvt. util. We have discussed a DFS solution for islands is already discussed. Learn to code interactively with step-by-step guidance. Strongly Connected Components Applications. In the adjacency list representation, we have an array of linked-list where the size of the array is the number of the vertex (nodes) present in the graph. ; Start at a random vertex v of the graph G, and run a DFS(G, v). By using our site, you We can pick any of the remaining two edges. Our task now is to pre-compute the non-trainable part, so lets see how to do it. What we want is to somehow aggregate the feature information from the neighbouring nodes because we want to learn the embeddings that reflect graph neighbourhoods. For this article, my goal is to dive under the hood of GCNs and provide some intuition into what is happening in each layer. Hence, when the connected nodes have a lot of other connections (i.e. Ace your Coding Interview. Submit Rating . 2022 Studytonight Technologies Pvt. In this tutorial, you will learn how strongly connected components are formed. In the case of a digraph, you can think of the connections as one-way streets along which traffic can flow only in the direction indicated by the arrow. Example : In the below adjacency list we can see. For example, there exist two paths [03467] and [03567] from vertex 0 to vertex 7 in the following graph. stellargraph implements these computations in sparse format because of speed, so well follow their step and use their implementation. In the previous blogs weve looked at graph embedding methods that tried to capture the neighbourhood information from graphs. For a directed graph the only change would be that the linked list will only contain the node on which the incident edge is present. Also, you will find working examples of Kosaraju's algorithm in C, C++, Java and Python. For instance: dictionary_graph= {'A': {'C':5,'D':1,'E':2},'E': {'A':2,'F':3},'D':} Make sure the graph has either 0 or 2 odd vertices. We strongly recommend first reading the following post on Euler Path and Circuit. Before, we look into the details of this algorithm, lets have a quick overview about the following: cost is a 2-D array, representing the cost adjacency matrix for the graph; For some tasks this information might be crucial, so today well cover Graph Convolutional Networks (GCN) which can use both - graph and node feature information. NetworkX Package Python Graph Library. Push all the adjacent and unvisited vertices in the queue and mark them as visited. Such graph with only one connected component is called as Strongly Connected Graph. stellargraph has its own graph data structure that has a lot of cool functionalities and is required to work with their API. Given a Weighted Directed Acyclic Graph (DAG) and a source vertex s in it, find the longest distances from s to all other vertices in the given graph.. Lets start by reading in data. Given a directed graph and two vertices (say source and destination vertex), determine if the destination vertex is reachable from the source vertex or not. adjacency_list () [source] Return an adjacency list representation of the graph. If any of the adjacent elements is the destination return true. There are two ways in which we represent graphs, these are: Both these have their advantages and disadvantages. For example, the graph shown below has three connected components. 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