Every transaction directly references two previous transactions. But I was wondering, does this also mean that every transaction will be referenced by exactly two transactions or will it be random? If it is random, what does the distribution look like?
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They will have to be referenced by at least one transaction to give them a chance of being confirmed. Some transactions (e.g. milestones) will be approved by very many transactions), while others only have one. I don't have a full node handy so I'll wait for someone else who wants to write a script to evaluate this :-)– mihi ♦Commented Feb 7, 2018 at 19:37
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Let us assume every transaction directly references exactly k other transactions (k = 2 in the case of IOTA). Now under uniform random tip selection, every transaction will on average be referenced by k other transactions (due to the stationarity property).
The histograms below provide a visual proof of this. I assumed a network delay of h = 1 with 40k transactions per simulation. For comparison purposes, I am including two examples for the issue-rate λ (10 and 20).
