Euclidean distance was 66%, 32%, and 79% for the CHUV, NKI, and HCP datasets, respectively. Lastly, a recent study used both Euclidean distance and the measured length of axons in a geometric generative model of the mouse connectome Rubinov et al. (2015), finding no change in their results. For these reasons, we assert that Euclidean distance, though imperfect, is a reasonable proxy for the cost of forming a connection. 

Nonetheless, we felt it prudent to test the effect of using fiber length in place of Euclidean distance in our models. To do so we first constructed an interpo- lated fiber length matrix. The elements of this matrix contain fiber length esti- mates for the hypothetical tracts linking the pair of nodes, u and v . To obtain such estimates for nodes u and v , we calculate the Euclidean distance, E ( u, v ) between their respective centroids. We then consider all geometric neighbors of u and all geometric neighbors of v , where a geometric neighbor of u is any other node whose centroid is less than E ( u, v ) × τ away from that of u . Here, we use a fixed value τ = 0 . 2. The fiber length of the hypothetical connection between nodes u and v is set equal to the mean fiber length of connections between u and any of u ’s geometric neighbors and v and any of v ’s geometric neighbors. If no connections exist between these subsets of nodes, then we used the β coef- ficients from the Euclidean distance versus fiber length linear regression model to estimate a fiber length. 

## 5.6. CHUV Group-average matrix with exponential rule - See Figure S12 

In the main text we modeled the geometric wiring rule as a power-law func- tion. However, recent work has suggested that an exponential function better captures the relationship between edge length and connection probability (Hen- derson and Robinson, 2014). To this end, we replaced the geometric power-law function in our geometric models with an exponential function and re-ran our analyses. 

