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Copy file name to clipboardexpand all lines: docs/docs/advanced-topics/path-based-transactions.md
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## Flow Matrices
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Flow matrices are the mathematical representation of these path-based transactions. They describe the movement of Circles tokens through the network for a given transaction (or a batch of transactions).
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Flow matrices are structured representations for these path-based transactions. They describe the movement of Circles tokens through the network for a given transaction (or a batch of transactions).
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### Structure of a Flow Matrix
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4.**Streams**: A stream represents the actual intent of a sender to send an amount of Circles to a receiver - without specifying which Circles to send or over which path, simply that the receiver only ever receives Circles they trust. A stream specifies a `sourceCoordinate` as the index of the source (or sender) in the flow vertices array, an array of the `flowEdgeIds` to cross-reference with the flow edges the correct terminal edges of this stream; and `bytes data` that will be sent to the receiver of the stream in the acceptance call. A flow matrix can have:
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- zero streams provided: All edges combined must form a closed path where no sender and no receiver nett-receives or nett-sends an amount of Circles. This can be used to reorganise the balances of Circles across the graph.
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- one stream provided: The flow matrix represents the path of a single intended transfer between a sender and receiver.
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- two or more streams: The flow matrix represents a batch of intents of multiple senders to send Circles to receivers as a single path settled (while still performing the acceptance checks for each stream's receiver).
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- two or more streams: The flow matrix represents a batch of intents of multiple senders to send Circles to receivers, and they get settled on-chain as single path (while still performing the acceptance checks for each stream's receiver).
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### An example of a flow matrix
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E: Eva
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```
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Let's assume Alice wants to send 3 CRC to David, and 5 CRC to Eva. Bob wants to send 4 CRC to David as well. Let's assume they have the following trust graph among them.
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Let's assume Alice wants to send 3 CRC to David, and 5 CRC to Eva. Bob wants to send 4 CRC to David as well. Let's assume they have the following trust graph among them (where the arrow means "trusts"):
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