Abstract
Communication of signals among nodes in a complex network poses fundamental problems of efficiency and cost. Routing of messages along shortest paths requires global information about the topology, while spreading by diffusion, which operates according to local topological features, is informationally “cheap” but inefficient. We introduce a stochastic model for network communication that combines local and global information about the network topology to generate biased random walks on the network. The model generates a continuous spectrum of dynamics that converge onto shortest-path and random-walk (diffusion) communication processes at the limiting extremes. We implement the model on two cohorts of human connectome networks and investigate the effects of varying the global information bias on the network’s communication cost. We identify routing strategies that approach a (highly efficient) shortest-path communication process with a relatively small global information bias on the system’s dynamics. Moreover, we show that the cost of routing messages from and to hub nodes varies as a function of the global information bias driving the system’s dynamics. Finally, we implement the model to identify individual subject differences from a communication dynamics point of view. The present framework departs from the classical shortest paths vs. diffusion dichotomy, unifying both models under a single family of dynamical processes that differ by the extent to which global information about the network topology influences the routing patterns of neural signals traversing the network.
Highlights
The function of many real world complex networks is to relay information within and between their constituent elements
Brain network communication is typically approached from the perspective of the length of inferred paths and the cost of building and maintaining network connections
The implications are that the extent to which brain regions can be characterized as highly efficient or central, is dependent upon the assumptions under consideration, here instantiated by a single parameter that controls the extent to which knowledge about the global network topology shapes the dynamics. With this framework we explore a family of communication models that have not been previously explored in the context of brain communication, and postulate that future investigations of brain communication dynamics should take into consideration the impact that functional demands and the availability of metabolic resources may have on the repertoire of routing patterns taking place on the network
Summary
The function of many real world complex networks is to relay information within and between their constituent elements. Information transfer that takes place through topologically shortest paths is both fast and direct, and reduces a message’s vulnerability to errors and attack [4]. Such a communication model has disadvantages: it discounts the vast majority of a network’s structural connections [5,6], it is prone to bottlenecks and congestion [7,8,9], and it lacks robustness to edge failures [10]. A system’s ability to route along shortest paths relies on all of the system’s elements having information about the global topology of the network [11,12]. We refer to the cost of the information necessary for signal routing as the informational cost
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