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Designing algorithms that generate networks with a given degree sequencewhile varying both subgraph composition and distribution of subgraphs aroundnodes is an important but challenging research problem. Current algorithms lackcontrol of key network parameters, the ability to specify to what subgraphs anode belongs to, come at a considerable complexity cost or, critically, samplefrom a limited ensemble of networks. To enable controlled investigations of theimpact and role of subgraphs, especially for epidemics, neuronal activity orcomplex contagion, it is essential that the generation process be versatile andthe generated networks as diverse as possible. In this paper, we present twonew network generation algorithms that use subgraphs as building blocks toconstruct networks preserving a given degree sequence. Additionally, thesealgorithms provide control over clustering both at node and global level. Inboth cases, we show that, despite being constrained by a degree sequence andglobal clustering, generated networks have markedly different topologies asevidenced by both subgraph prevalence and distribution around nodes, andlarge-scale network structure metrics such as path length and betweennessmeasures. Simulations of standard epidemic and complex contagion models onthose networks reveal that degree distribution and global clustering do notalways accurately predict the outcome of dynamical processes taking place onthem. We conclude by discussing the benefits and limitations of both methods.

Generation and analysis of networks with a prescribed degree sequence and subgraph family: Higher-order structure matters