NETWORK.CYCLES OpenBI

Round trips: cycles in the network, as money moving in a circle.

Group: Networks. OpenBI’s own: DAX has no function of this name.

Syntax

NETWORK.CYCLES ( <links>, <from>, <to> [, <weight>] [, <directed>] [, <longest>] )

Parameter	Type	Description
`links`	Table	The rows that make the network, one link a row: a table of the model or a table expression, as the filters leave it.
`from`	Expression evaluated for each row	One end of each row's link, such as a payer, a customer or a place.
`to`	Expression evaluated for each row	The other end of each row's link.
`weight`	Expression optional, evaluated for each row	How heavy each row's link is, such as an amount or a count; never negative. Left out, or given as the constant BLANK (), every row weighs 1.
`directed`	Boolean optional	TRUE when each link runs one way, from its first end to its second. FALSE or left out, a link works both ways.
`longest`	Whole number optional	The most links a cycle may have, from 2 to 20: 6 when left out.

Returns

Table. A row a step of each cycle. Its columns: Cycle and Length; Step, Node and Next; Weight and Least weight.

Remarks

A cycle goes from node to node along the links and comes back to where it started, visiting no node twice. Each cycle is listed once, its steps in order: Node pays Next, and Weight is that link's weight.
Least weight is the smallest weight on the cycle, on every row of it: the most that can have gone all the way round.
Directed, a cycle follows the links' direction and can be as short as 2 (A pays B, B pays A). Not directed, a cycle has at least 3 links.
At most 10,000 cycles are listed. On a large, dense network keep longest small, or filter the rows first.
Several rows between the same two nodes make one link, and their weights add up. Without a weight each row adds 1, so a pair that appears three times weighs 3.

Compared with DAX

An OpenBI function: DAX has none like it, so a measure or query that uses it works in OpenBI only, not in Power BI or Analysis Services.

Examples

Money going round

Two rings: A, B and C, and C, D and E. At most 60 can have gone round the first, 30 the second.

EVALUATE
VAR Payments =
    DATATABLE (
        "Payer", STRING, "Payee", STRING, "Amount", INTEGER,
        {
            { "A", "B", 100 }, { "B", "C", 80 }, { "C", "A", 60 }, { "C", "D", 50 },
            { "D", "E", 40 }, { "E", "C", 30 }, { "E", "F", 20 }
        }
    )
RETURN
    SELECTCOLUMNS (
        NETWORK.CYCLES ( Payments, [Payer], [Payee], [Amount], TRUE ),
        "Cycle", [Cycle],
        "Step", [Step],
        "Node", [Node],
        "Next", [Next],
        "Weight", [Weight],
        "Least weight", [Least weight]
    )

Cycle	Step	Node	Next	Weight	Least weight
1	1	A	B	100	60
1	2	B	C	80	60
1	3	C	A	60	60
2	1	C	D	50	30
2	2	D	E	40	30
2	3	E	C	30	30

Triangles of friends

EVALUATE
VAR Links =
    DATATABLE (
        "From", STRING, "To", STRING,
        {
            { "Ann", "Bo" }, { "Ann", "Cy" }, { "Bo", "Cy" }, { "Cy", "Di" },
            { "Di", "Ed" }, { "Ed", "Fay" }, { "Di", "Fay" }, { "Fay", "Gus" }
        }
    )
RETURN
    SELECTCOLUMNS (
        NETWORK.CYCLES ( Links, [From], [To] ),
        "Cycle", [Cycle],
        "Length", [Length],
        "Node", [Node]
    )

Cycle	Length	Node
1	3	Ann
1	3	Bo
1	3	Cy
2	3	Di
2	3	Ed
2	3	Fay

NETWORK.TRIADS, NETWORK.CLIQUES, NETWORK.REACH, NETWORK.FLOW.

Open Graph, OpenBI's graph library, does the work: simple_cycles. See the OAX network functions and Open Graph.

Last updated 6 November 2026 · OpenBI Studio 0.3.78