Analytically tractable model of synaptic crowding explains emergent small-world structure and network dynamics

Neural circuits must balance local connectivity constraints against the need for global integration. Here we introduce a minimal wiring rule motivated by synaptic crowding: as a neuron accumulates incoming connections, each additional synapse becomes progressively harder to form. This single-parameter model admits an exact finite-size solution for the induced in-degree distribution and yields simple scaling laws: mean connectivity grows only logarithmically with network size while variance remains bounded -- consistent with homeostatic regulation of synaptic density. When candidates are encountered in order of spatial proximity, the crowding rule produces a broad, approximately power-law distribution of connection lengths without prescribing any explicit distance-dependent wiring law; combined with shortcut rewiring, this yields networks with small-world characteristics. We further show that the induced degree statistics largely determine attractor basin boundaries in threshold network dynamics, while local clustering primarily modulates the prevalence of long-lived non-absorbing outcomes near these boundaries. The model provides testable predictions linking local developmental constraints to macroscopic network organization and dynamics.