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I am studying adjacency matrix and I have the following question: Can an adjacency matrix have all their entries equal zero?

From what I understand it has zeros in its main diagonal and the other entries can be zero or one.

if there exists a path is 1 and 0 otherwise.

So I assume that from these definitions, it is not possible.

Can anyone help me on this?

Thanks

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What's the adjacency matrix of the graph with $n$ vertices whose edge-set is empty?

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    'An empty graph on nodes consists of isolated nodes with no edges' so it is possible right? – 2017-02-18
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    If you have a graph with no edges then all the entries in adjacency matrix are zero. You might want to rewrite your question ... 1 if there is an edge ... There will be a path if there is a power of the adjacency matrix that has a non zero entry. – 2017-02-18
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    Wouldn't an adjacency "matrix" on a graph with zero vertices be an "empty matrix"? I think you rather want to consider the adjacency matrix of a graph with $n$ vertices and no edges. – 2017-02-18
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    @JoshuaRuiter good point, I edited the answer. – 2017-02-18
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    The null graph? – 2017-02-27