Tree decompositions and social graphs
Aaron B. Adcock, Blair D. Sullivan, Michael W. Mahoney

TL;DR
This paper empirically evaluates tree decomposition heuristics on social graphs, demonstrating their ability to identify meaningful structures like core-periphery and communities, and provides theoretical insights into hyperbolic embedding limitations.
Contribution
It shows that existing tree decomposition heuristics can effectively reveal structural properties of social networks and offers a theoretical framework explaining embedding challenges.
Findings
TD methods correlate with core-periphery structures
Peripheral bags align with low-conductance communities
Ground-truth communities are localized in TD structures
Abstract
Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical evaluation of the use of tree decomposition (TD) heuristics for structure identification and extraction in social graphs. Although TDs have historically been used in structural graph theory and scientific computing, we show that---even with existing TD heuristics developed for those very different areas---TD methods can identify interesting structure in a wide range of realistic informatics graphs. Our main contributions are the following: we show that TD methods can identify structures that correlate strongly with the core-periphery structure of realistic networks, even when using simple greedy heuristics; we show that the peripheral bags of these TDs…
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