Is this still not possible in 2019?
What is your use case for publishing a network dataset to AGOL? Thanks,
Jay Sandhu
I work for a government agency representing the Chicago metropolitan region. We have a network dataset for pedestrian infrastructure (sidewalks and other off-street pedestrian paths) that we use internally for pedestrian routing and walkshed (service area) analyses. We would like to be able to share this capability with our constituents who do not have access to or knowledge of GIS software.
So looks like you have some routing service (that utilize your network dataset) that you would like to expose to your constituents.
The way it is supported is to publish your routing services on your own server (using publishing routing services utility). You can then use a geoprocessing widget with web app builder in AGOL to create a web app that exposes your service to your constituents.
More on the publishing utility and web app builder here:
Publish Routing Services utility—ArcGIS Server Administration (Linux) | ArcGIS Enterprise
Web AppBuilder for ArcGIS | ArcGIS
Jay Sandhu