Detrimental role of fluctuations in the resource dependency networks

Abstract: Individual components of many real-world complex networks produce and exchange resources among themselves. However, because the resource production in such networks is almost always stochastic, fluctuations in the production are unavoidable. In this paper, we study the effect of fluctuations on the resource dependencies in complex networks. To this end, we consider a modification of a threshold model of resource dependencies in networks that was recently proposed, where each vertex has a fitness that depends on the total amount of resource it has produced, the amount it has procured from its neighbours, and the fitness threshold. We study how the ``network fitness'', defined as the average fitness of vertices in the network, is affected as the fluctuation size is varied. We show that the fluctuations worsen the network fitness even when average production on vertices is kept fixed. This is true independent of whether more than required amount is produced in the network or not. However, this effect saturates for large fluctuations, and hence very large fluctuations cannot worsen the network fitness beyond a limit. We further show that the networks with a homogeneous degree distribution, such as the Erdos-Renyi network, are less affected by fluctuations and also produce lower wastage than the networks with a heterogeneous degree distribution like the Scale-Free network. Our work shows that fluctuations in the resource production should be avoided in resource dependency networks.