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## 2.2. Generative algorithm 

In this report we generate synthetic networks using a generative model. The algorithm for producing synthetic networks is simple. Starting with a sparse seed network (62 bi-directional edges that were common across all 40 participants), edges were added one at a time over a series of steps until M total connections were placed (where M = 576 ± 57 connections across subjects). At each step we allow for the possibility that any pair of unconnected nodes, u and v , will be connected. Connections are formed probabilistically, where the relative probability of connection formation is given by: 

In this expression E ( u, v ) denotes the Euclidean distance between brain re- gions u and v . The exponent η controls the characteristic connection length. When η < 0, short-range connections are favored, while η > 0 increases the probability of forming longer connections. The other term, K ( u, v ), represents an arbitrary non-geometric relationship between nodes u and v and the value of γ scales its relative importance. The precise definition of K ( u, v ) is flexi- ble and can be varied to realize different wiring rules. For instance, setting K ( u, v ) = k$_{u}$k$_{v}$ and γ > 0 implements a variant of preferential attachment, wherein higher degree nodes are more likely to become connected. Alterna- tive definitions can be used to implement rules such as degree assortativity (e.g. K ( u, v ) = | k$_{u}$ − k$_{v}$ | , where nodes with similar/dissimilar numbers of connections preferentially connect to one another) or homophily (e.g. K ( u, v ) = $^{∑}$$_{w}$a$_{uw}$ a$_{wv}$ where connections form between nodes with more or fewer common neighbors). In Table 1 we show a complete list of all non-geometric wiring rules. We limit our analysis to generative models whose wiring rules include only two components, though we could accommodate more components, in principle. We impose this 

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