Multiple realities
(covers information from several alternate timelines)

A transwarp network, sometimes spelled as trans warp network, was the term used of networked transwarp connections in space. (VOY: "Endgame"; Star Trek Into Darkness, display graphic)

Borg transwarp network

The Borg transwarp network

The Borg transwarp network in the 24th century was a vast series of transwarp conduits spanning the entire Milky Way Galaxy. The conduits in the network were connected by 6 transwarp hubs, and were supported by a series of interspatial manifolds, which were protected by shielding regulated from the central nexus by the Borg Queen herself. The network maintained thousands of exit apertures in all four quadrants, allowing the Collective to deploy vessels almost anywhere in the galaxy within minutes, giving the Borg a decisive strategic advantage.

The transwarp network was destroyed in 2378 when Kathryn Janeway's counterpart from 2404 was able to infect the Queen with a neurolytic pathogen, an act which interfered with the Queen's ability to regulate the shielding protecting the interspatial manifolds. This in turn allowed the crew of the USS Voyager to fire a series of transphasic torpedoes, destroying the manifolds and causing the network to collapse. (VOY: "Endgame")

There were some discrepancies between the display graphic of the network and the dialogue about it. According to dialogue there were six transwarp hubs in the galaxy, while the graphic only showed four hubs, one in each quadrant. Additionally, according to dialogue, there were only exit apertures in the Alpha Quadrant, while the graphic shows a hub in the Alpha Quadrant as well.

Federation transwarp network

In the alternate 2259, the Federation had an experimental trans warp network in the Alpha Quadrant. The network, resembling a triangle, had three points resembling hollow yellow-bordered pentagons. One of the routes was a corridor. This network was labeled on a map depicting a section of the Alpha Quadrant. This map was seen on a powerwall in the offices of Admirals Christopher Pike and Alexander Marcus at Starfleet Headquarters. (Star Trek Into Darkness)

The meaning of the pentagons is not defined in the map. As the result of the two-dimensional nature of the map, it is not possible to know the network's location in relation to the Neutral Zone. The map is visible in the video "Star Trek: Into Darkness – User Interface VFX at [1]
In the comic book stories, set in 2259 before Star Trek Into Darkness, "The Truth About Tribbles, Part 1" and "Part 2", on which the films screenwriter Roberto Orci served as a creative consultant, Scotty successfully experiments with extreme long-range transwarp beaming. He sends his pet tribble back to Earth from the Iota Geminorum system by bouncing the beam off relays along the way. Scotty explains the intention of creating this networked transwarp beaming was to allow Starfleet to beam living things between Earth and the fleet stationed in deep space. It's possible, that the transwarp network on the map shows the relay stations and the routes of transwarp beaming.
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