Spectral clustering based on the random-walk transition matrix identifies high-effective-information macro-scales of preferential attachment networks faster than greedy or gradient-descent search.
The emergence of informative higher scales in complex networks
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abstract
The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and certainty) contained in paths along nodes and links in a network. Specifically, we derive from first principles a measure known as effective information and describe its behavior in common network models. Networks with higher effective information contain more information in the relationships between nodes. We show how subgraphs of nodes can be grouped into macro-nodes, reducing the size of a network while increasing its effective information (a phenomenon known as causal emergence). We find that informative higher scales are common in simulated and real networks across biological, social, informational, and technological domains. These results show that the emergence of higher scales in networks can be directly assessed and that these higher scales offer a way to create certainty out of uncertainty.
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2019 1verdicts
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Finding the right scale of a network: Efficient identification of causal emergence through spectral clustering
Spectral clustering based on the random-walk transition matrix identifies high-effective-information macro-scales of preferential attachment networks faster than greedy or gradient-descent search.