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## 3.2. Models driven by geometry and topology outperform pure geometric models 

The failure of the pure geometric model to generate synthetic networks that were as clustered and contained as many long-distance connections as observed connectomes suggests that additional factors are needed as part of a realis- tic generative mechanism. To determine which factors were most capable in this regard we compared twelve different generative models where topological features such as degree, clustering, and homophily influenced the connection formation probabilities. As expected, due to the additional free parameter, γ , we find that all dual-factor models outperformed the pure geometric model, gen- erating synthetic networks with significantly lower energies ( p ≈ 0, see Figure 2). Importantly, dual-factor models were stratified, with clustering-based mod- els outperforming degree-based models, which in turn were outperformed by homophily-based models. The absolute best model incorporated a homophilic attraction mechanism in the form of the matching index (MI), which is a nor- malized measure of overlap in two nodes’ neighborhoods. If Γ$_{u}$ = { v : a$_{uv}$ = 1 } represents the set of node u ’s neighbors, then the matching index is equal to: 

where Γ$_{u}$$_{\}$$_{v}$ is simply Γ$_{u}$ but with v excluded from the set. In the event that u and v have perfect overlap in their neighborhoods, then M$_{uv}$ = 1. If the neighborhoods contain no common elements then M$_{uv}$ = 0. 

Applied to the CHUV dataset, the MI model achieved an average energy of E = 0 . 12 ± 0 . 02 with parameters η = − 0 . 98 ± 0 . 37 and γ = 0 . 42 ± 0 . 04 (Figure 3C). Together, these parameter values indicated that, like the pure geometric model, the MI model exercised a penalty against long distance con- nections (albeit markedly weaker than the geometric model), while increasing the probability that nodes with similar connectivity profiles would connect to 

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