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I've observed the ratio of transaction count and operation count for a while and there is high fluctuation in the relationship between them. Could someone explain me how the ratio reflects the growth of Stellar?

Thanks in advance.

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Each transaction can contain up to 100 operations (this number may be changed in the future). For the most basic operations (peer-to-peer funds transfer, orders on the Stellar exchange) it's almost always a 1:1 ratio.

However, there are a lot of cases when anchors or any other applications combine multiple operations into the single transaction. For example, market making usually implies that you maintain at least a pair orders (bid and ask). So it's only natural to combine all order manipulations in single tx. Mass payouts scheme (for example, payments from inflation pools) is another example of this case.

I don't think that transaction/operation ratio has any correlation with the network growth. Maybe the activity of apps (bots if you like) vs regular users at most.

If you are looking for the growth indicators, it seems to me that the number of active accounts, total trustlines count, and number of trades vs number of transfers are better suited for your needs. You can find all these indicators with retrospective at stellar.expert.

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