Random walk patterns to identify weighted motifs
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Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real complex systems. Particularly relevant in this sense appears the identification of significant subgraphs that can shed light onto the underlying evolutionary processes. Such patterns, called motifs, have received much attention in binary networks, but a similar deep investigation for weighted networks is still lagging behind. Here, we proposed a novel methodology based on a random walker and a fixed maximum number of steps to study weighted motifs of limited size. The novelty is represented by the introduction of a sink node to balance the network and allow the detection of configurations within an a priori fixed number of steps for the random walker. We applied this approach to different real networks and selected a specific benchmark model based on maximum-entropy to test the significance of weighted motifs occurrence. We found that identified similarities enable the classifications of systems according to functioning mechanisms associated with specific configurations.
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