Graph-theory-question - Advanced Questions

Topic: Graph-theory-question / Level: Advanced

580. Implement a function to compute the flow network's minimum cut.
581. Write a program to find the shortest path in a directed graph with negative weights.
582. Create a function to compute the average clustering coefficient for a directed graph.
583. Write a program to determine the number of edges needed to connect all components in a directed graph.
584. Implement an algorithm to find the longest path in a tree.
585. Write a program to check if a directed graph is acyclic.
586. Create a function to compute the distance matrix for a directed graph.
587. Write a program to find the longest increasing path in a tree.
588. Implement a function to determine the longest path that visits every vertex in a directed graph.
589. Write a program to compute the betweenness centrality for a directed graph.
590. Create a function to check if a directed graph has a unique Eulerian circuit.
591. Write a program to find the longest path in a directed graph using depth-first search.
592. Implement an algorithm to compute the maximum flow in a directed graph.
593. Write a program to determine the longest path in a directed acyclic graph.
594. Create a function to compute the reachability from a single source in a directed graph.
595. Write a program to find the shortest path in a directed graph using the A* search algorithm.
596. Implement a function to compute the average distance between all pairs of vertices in a directed graph.
597. Write a program to check if a directed graph can be made acyclic.
598. Create a function to compute the longest path in a directed graph with positive and negative weights.
599. Write a program to find the minimum spanning tree of a directed graph.

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Create a function to determine the minimum cut in a flow network using the Stoer-Wagner algorithm. Write a program to calculate the degree distribution of a graph. Write a program to perform a breadth-first search (BFS) in a graph and return the traversal order. Write a program to check if a tree is a valid binary search tree. Write a program to check if a directed graph has a unique shortest path between two vertices. Write a program to find the maximum flow in a flow network using the Edmonds-Karp algorithm. Write a program to implement Dijkstra's algorithm for finding the shortest path in a weighted graph. Write a program to compute the reachability matrix of a directed graph. Write a program to compute the betweenness centrality for all vertices in a graph. Write a program to find the k-th shortest path in a weighted graph. Write a program to determine if a graph is a valid tree. Write a program to check if a graph can be colored with three colors. Implement an algorithm to compute the convex hull of a set of points. Write a program to find the longest cycle in a directed graph. Write a program to compute the betweenness centrality for a graph.