A topological graph is a CW complex with only zero-cells and one-cells, called vertices and edges. Edge endpoints attach to vertices; loops, multiple edges and infinitely many edges are allowed. A subgraph in this setting is a CW subcomplex. A connected acyclic graph is a tree and is a contractible space.
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In the context of mathematics, particularly in topology, a **graph** can refer to a couple of concepts, depending on the context—most commonly, it refers to a collection of points (vertices) and connections between them (edges). However, it might also refer to specific topological constructs or the study of graphs within topological spaces. Here’s a breakdown of what a graph generally signifies in these contexts: ### 1.