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The edges of a network represented by linear bonds constitute linear constraints on the coordinates of the vertices. In atomic networks, angular bonds give rise to additional constraints at the vertices. The linear and angular constraints, together, are called bond constraints. Since an angular constraint can be viewed simply as the result of an additional cross‐linear bond between next‐nearest neighbors, the linear and angular constraints carry equal weights. In other words, during constraint counting, one angular constraint and one linear constraint add up to two constraints.

It is important to distinguish between independent and dependent (or redundant) constraints. Constraints in a network that do not change its deformation behavior are called dependent. Consider, for example, a finite planar network of four nodes situated at the corners of a square (Figure 1) for which the sides constitute four linear constraints. If these are the only constraints present, the network is floppy (i.e. it can be deformed). When a diagonal constraint is added, however, the network becomes rigid. When a second diagonal is added as the sixth constraint, no further change occurs in the deformation behavior of the network – it remains rigid. The sixth constraint, in this example, is therefore a dependent constraint. In TCT, it is important to count only the independent constraints and to exclude the dependent. To determine whether a constraint is dependent or not can be a challenging task. Owing to the presence of long‐range topological order, crystalline networks contain a significant number of dependent constraints. Whereas one has to be extremely careful in applying constraint theory to crystals, this is fortunately not the case in noncrystalline TD networks.

Figure 1 Deformation of a finite network of four nodes. Lines represent linear constraints. Top: floppy network (hypostatic, f > 0) with only four constraints originating from the edges. Middle: addition of a diagonal constraint makes the network rigid (isostatic with f = 0). Bottom: addition of a second, dependent diagonal constraint does not change the rigidity of the network.