There are a few ways that I can think of to do this. The easiest way to do this would be to swap the ACTIVITY and SUCCESSOR variables like what has been suggested. If you are using the default variables _FROM_ and _TO_ you would need to rename these accordingly.
Another way would be to use the Layout data set, which you can output using the LAYOUT= option in the ACTNET statement. For more details, see the "Layout Data Set" and "Controlling the Layout" in the details section.
https://go.documentation.sas.com/?docsetId=orpmug&docsetTarget=orpmug_netdraw_details07.htm&docsetVersion=15.2&locale=en
https://go.documentation.sas.com/?docsetId=orpmug&docsetTarget=orpmug_netdraw_details08.htm&docsetVersion=15.2&locale=en
A third option would be to use the Annotate facility that Netdraw supports. You would likely need to specify ARROWHEAD=0 in the ACTNET statement to suppress the default arrowhead. While this approach provides more customization capabilities, it also would require a bit more effort. Hope this helps.
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