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Is this sentence correct (especially the usage of whom)?

In addition, it might jump to a random vertex in the graph, whom the current vertex is not necessarily connected to, with a certain probability.

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No, the writer should use "which" instead of "whom." It is also not clear what the "with a certain probability" clause refers to.

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In addition, it might jump to a random vertex in the graph to which the current vertex is not necessarily connected, with a certain probability.

Removing the comma after graph shows that the "with a certain probability" clause refers to "it" jumping, and not to its connection to the "current vertex." Am I understanding that clause?

Or you could try:

In addition and with a certain probability, it might jump to a random vertex in the graph to which the current vertex is not necessarily connected.

Apologies if I'm not understanding that final clause.

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The word "whom" is the objective form of "who" which is used in reference to persons. So unless the vertex is connected to a person, it is not correct to use it.

The word "which" probably would be better.

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