The phrase "a network of paths" is correct and usable in written English.
It can be used to describe a system or arrangement of interconnected routes or trails, often in the context of geography, transportation, or metaphorical frameworks.
Example: "The park features a network of paths that allow visitors to explore its natural beauty."
Alternatives: "a system of trails" or "an interconnected series of routes."
Below the plaza, a network of paths winds along the hills beneath the great parapeted embankments.
These communities, consisting of 30 or more houses connected by a network of paths, were built along the coast.
A network of paths wanders by plantings of desert-adapted trees, shrubs, wildflowers and cactuses -- all of which provide a bonanza for insects and hummingbirds.
The community, which has some residents, advertises "a healthy lifestyle and simplified living," including gardens, pocket parks and a network of paths.
A 40-foot-high arched torii gateway marks your entry into this spiritual world, and a network of paths leads to the shrine.
A network of paths take you across the surrounding countryside and into the Brocéliande forest, 25 square miles of woodland that's full of legends about King Arthur and Merlin.
It's not only Amsterdam which boasts a network of cycle-paths, of course; you'll find them in all Dutch cities.
City government provides a large number of recreational and leisure facilities for its citizens, including a large park in the center of the city, many smaller parks scattered through the city, a golf course, Alameda Park Zoo, a network of walking paths, Alamogordo Public Library, and a senior citizens' center.
The top of the mountain is navigated by a network of walking paths.
A network of brick paths wander through the garden, circling the fishpond, which is aerated (when it works) by a solar panel on top of a gazebo.
The first phase is simply a network of bicycle paths, complete with a storehouse of free bicycles that could be installed as soon as demolition is complete.
