Network Essence: PageRank Completion and Centrality-Conforming Markov Chains
Shang-Hua Teng

TL;DR
This paper explores the algebraic properties of personalized PageRank matrices, proposing a Markovian network completion approach to better understand the underlying essence of complex network data.
Contribution
It introduces a novel perspective on network analysis by emphasizing the algebraic properties of PageRank matrices and proposing a Markovian completion framework for network understanding.
Findings
Personalized PageRank matrices exhibit specific algebraic properties.
Markovian closure offers a new way to complete and analyze network data.
The approach motivates systematic development of network theory.
Abstract
Ji\v{r}\'i Matou\v{s}ek (1963-2015) had many breakthrough contributions in mathematics and algorithm design. His milestone results are not only profound but also elegant. By going beyond the original objects --- such as Euclidean spaces or linear programs --- Jirka found the essence of the challenging mathematical/algorithmic problems as well as beautiful solutions that were natural to him, but were surprising discoveries to the field. In this short exploration article, I will first share with readers my initial encounter with Jirka and discuss one of his fundamental geometric results from the early 1990s. In the age of social and information networks, I will then turn the discussion from geometric structures to network structures, attempting to take a humble step towards the holy grail of network science, that is to understand the network essence that underlies the observed…
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Taxonomy
TopicsComplex Network Analysis Techniques
