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Implementing graphs and initializing adjacency matrices

Graphs are often represented using an adjacency matrix. Various sources indicate that initialization costs can be avoided | V ^ 2 | (V is the number of vertices), but I could not figure out how to do this.

In Java, just declaring a matrix, for example. boolean adj [][]The runtime automatically initializes the array with false, and it will cost O (V ^ 2) (array sizes).
Do not I understand? Is it possible to avoid the quadratic cost of initializing the adjacency matrix, or is it just something theoretical that depends on the implementation language?

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