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CS Academy

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Now that we've seen what graphs are and how we can represent them visually, we'll take a look on the ways we can write a program that uses them. We will present two methods of working with graphs and compare their advantages and disadvantages. Suppose we have a directed graph with 𝑁 N vertices. We can use 𝑁 ∗ 𝑁 N∗N binary matrix, where the element on row 𝑖 i and column 𝑗 j is 1 1 if the arc ( 𝑖 , 𝑗 ) (i,j) exists in the graph, and 0 0 otherwise. Below you can see a graph and its corresponding adjacency matrix: 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 Notice that in the example above the graph was directed, so each arc had a unique corresponding entry in the matrix. But what if the graph were undirected? How could it be represented using an adjacency matrix? The answer is simple, each edge ( 𝑖 , 𝑗 ) (i,j) will have two corresponding entries in the matrix, both cell ( 𝑖 , 𝑗 ) (i,j) and cell ( 𝑗 , 𝑖

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