Structuring precedes extension in percolating Physarum polycephalum networks

Microplasmodia of the slime mold Physarum polycephalum form a small link degree transportation network in a percolation transition in order to forage. We model this transition analytically within the configuration model of graph theory utilizing all partaking types of nodes. Quite generally, we find that at the percolation transition the formation of a small link degree network is topologically highly constrained and only weakly dependent on environmental factors. Structuring of the network as characterized by global efficiency and centrality measures precedes area search in order to forage.