Is there any connection between the computer science phrase "[network topology](https://en.wikipedia.org/wiki/Network_topology)" and the mathematical notion of a [topological space](https://en.wikipedia.org/wiki/Topological_space) (or, is there any other way to connect "network topologies" with formal definitions from the field of topology)?

Example: I suppose that if one said "there are two nodes A and B, and they are each connected to a third node C, and C is connected to a fourth node D, and D is node E and D is also connected to node F, and the names of A and B are "A" and "B", and the name of C is 'LAN router' and the name of D is 'ISP AP' and the name of E is 'Website 1' and the name of F is 'Website 2'", then the mathematical name for that sort of structure would be a "graph with labeled nodes". In addition, if one assigned a directionality to each link, eg "F > D, E > D, D > C, C > A, C > B", then this would make it a "directed graph with labeled nodes". And if some nodes had multiple ports, and each node gave locally unique names to each port, that would induce a unique naming on edges (the name of an edge is the 4-tuple (source node's name, source node's port, destination node's name, destination node's port)), and you could call it a "directed graph with labeled nodes and edges". All of these appear to me to fit within the computer science term "network topology", and all of the mathematical terms given above which appear to be from "graph theory". I am just unclear if these have anything to do with the mathematical area of "topology".

Also, does the phrase "network topology" have anything to do with "topological graph theory" or with abstract simplicial complexes?

Possibly related: 

* [Etymology of "topological sorting"](https://math.stackexchange.com/questions/113288/etymology-of-topological-sorting/113411#113411) suggests that sometimes the word 'topology' is used in computer science in a sense unrelated (except historically) to the modern conception of topology.
* <https://en.wikipedia.org/wiki/Graph_theory#History> mentions various historical connections between topology and graph theory, but it is too general for me to tell specifically which topological definitions apply to graphs
* Near the top, [Wikipedia:Network topology](https://en.wikipedia.org/wiki/Network_topology) claims "Essentially, it (network topology) is the topological structure of a network".
* <https://en.wikipedia.org/wiki/Topological_graph_theory>
* <https://en.wikipedia.org/wiki/Abstract_simplicial_complex>
* [In a graph, connectedness in graph sense and in topological sense](https://math.stackexchange.com/questions/103633/in-a-graph-connectedness-in-graph-sense-and-in-topological-sense) and [Follow-up: Topology on graphs](https://math.stackexchange.com/questions/103702/follow-up-topology-on-graphs) appear to connect graph theory and topology, but only for the purpose of results about connectedness, not more generally to justify a graph as being definitionally equivalent to a 'network topology'.
* i don't see how a graph can be usefully considered equivalent to a topological space because if one took nodes to be points and the open sets to be the neighbors of each point, then because the union of open sets is open, then by taking any two points which are disconnected from each other on the graph, one can take the union of their open sets and call it an open set.