Political fragmentation denotes the differentiation of a political system into multiple groups and the extent of separation among them. It often manifests structurally in online interaction behaviors. To measure and compare political fragmentation across contexts, previous scholarship has often relied on network measures of polarisation such as modularity and the Krackhardt E-I index. Here, we show that these metrics combine two aspects of fragmentation: the strength of separation and the number of fragments. These two aspects have not been clearly distinguished in previous work, making comparisons across varied systems difficult to interpret. In addition, none of them is designed to capture the multiscale fragmentation structures that characterize real-world multi-dimensional political spaces. We compare several network measures and show that the two aspects of network fragmentation are best captured by the pairwise adaptive E-I index and the effective number of communities (ENC), while other measures confound the strength of separation and the number of fragments. Furthermore, we introduce a novel metric for multiscale fragmentation, the effective branching factor (EBF), capturing how political fragments at one level split into smaller fragments at the next level. Applying EBF to two empirical datasets spanning Brazil, Spain, and the United States yields consistent country rankings across datasets. Overall, these results clarify three complementary dimensions of structural political fragmentation: strength of separation, number of fragments, and between-level branching. They support a more holistic characterization of structural political fragmentation.