Sie Hendrata Dharmawan

Sie Hendrata Dharmawan, Kevin Limanta, Brendan Liu et al.

Node centrality is a fundamental problem in network analysis, yet classical metrics fail to capture the collective, coalitional nature of influence. We present a systematic empirical evaluation of the Shapley-value-based framework for the sphere of influence problem -- selecting $m$ nodes to maximize network coverage under three reachability criteria: single-hop, $k$-hop, and multi-path connectivity -- using exact polynomial-time algorithms due to Michalak et al. Evaluation across three diverse real-world networks (Euroroad, Facebook TV Shows, and Cora) demonstrates that practical approximation ratios consistently approach 0.9, substantially exceeding the theoretical $(1-1/e)$ lower bound, and that the Shapley-based approach dramatically outperforms a degree-based baseline, particularly in hub-and-spoke topologies. In the most striking case, Shapley-based selection identifies just 26 nodes (under 1\% of the Cora network) sufficient to influence half the graph under 3-hop reachability, compared to substantially larger sets required by the naive baseline.

Sie Hendrata Dharmawan, Peter Chin

We study community detection in the two-block stochastic block model under the setting where multiple independent graph samples drawn from the same distribution are available. Building on a recently simplified spectral algorithm that preserves the independence of adjacency matrix entries throughout, we show that averaging $m$ independent samples before applying spectral partitioning reduces the error bound $γ$ exponentially in $m$: specifically, one can find a $γ$-correct partition with probability $1 - o(1)$ whenever $\frac{(a-b)^2}{a+b} \geq \frac{C}{m} \log \frac{2}γ$, improving the single-sample requirement by a factor of $m$. The key technical contribution is a multi-sample analogue of the spectral norm bound on the noise matrix, which propagates through the Davis-Kahan subspace angle analysis to yield the improved recovery guarantee. We provide experimental validation across a range of graph sizes ($n$ up to $1000$) and sample counts ($m$ up to $9$), demonstrating that the derived bounds are sharp and that even two or three samples yield dramatic improvements in recovery accuracy. Our results offer a rigorous theoretical foundation for graph data augmentation strategies used in modern graph representation learning.

Sie Hendrata Dharmawan, Peter Chin

We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions. By reducing algorithmic complexity through the elimination of non-essential preprocessing steps, our method directly leverages the spectral properties of the adjacency matrix. We demonstrate that our algorithm exploits specific characteristics of the second eigenvalue to achieve improved error bounds that approach information-theoretic limits, representing a significant improvement over existing methods. Theoretical analysis establishes that our error rates are tighter than previously reported bounds in the literature. Comprehensive experimental validation confirms our theoretical findings and demonstrates the practical effectiveness of the simplified approach. Our results suggest that algorithmic simplification, rather than increasing complexity, can lead to both computational efficiency and enhanced performance in spectral community detection.