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Can two given neurons in the human brain can be directly connected more than once, either mutually or in the same or direction? Also, can the same neuron have transitive connections to itself (in order to amplify itself for example)?

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I guess the answer depends on what you mean with "connected more than once".

Initially, being connected is a strictly binary relation: either two neurons are connected or not. (The question may be: directly or not. Indirectly, each pair of neurons is connected, as I assume.)

If you consider "being connected more or less strongly" - which is not a binary relation anymore - you may consider the degree of connectedness as a natural number 1, 2, 3, ... and in this case, you might want to count synapses between two neurons. And surely, there can be more than one:

»An important experimentally observed feature [...] is the distribution of the number of synapses from one neuron to another, which has been measured in several cortical layers. All of these distributions are bimodal with one peak at zero and a second one at a small number (3–8) of synapses.«

If you want to consider pathways between two neurons A and B - shortest sequences of connected neurons starting with A and ending with B - then the answer is "yes, of course" again:

»[Each neuron] is within two or three connections of all the others via myriad potential routes.«

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  • $\begingroup$ Thanks for the answer. I was curious about direct connections, i.e. can there be two synapses each connecting neuron A to neuron B. $\endgroup$
    – danijar
    Commented Jan 8, 2020 at 23:45
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    $\begingroup$ So 3-8 is an answer in several cortical layers. $\endgroup$ Commented Jan 9, 2020 at 6:45

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