Structural Information Of Graphs Research Articles

CABGSI: An efficient clustering algorithm based on structural information of graphs

This paper introduces CABGSI, a novel graph-based clustering algorithm that effectively addresses the limitations of traditional clustering techniques. Unlike conventional methods that require predefined cluster quantities and assume simple geometrical data structures, CABGSI leverages graph structural entropy to naturally discern clusters. Our algorithm constructs a network among data points, capturing the intrinsic structure of the data. We demonstrate its superior performance on diverse datasets, particularly those with complex geometries such as speckles and images. Despite challenges with moon and ring configurations, CABGSI significantly outperforms traditional algorithms like k-means by not relying on predetermined cluster centers. This innovation broadens the applicability of clustering techniques and paves the way for future research in data analysis.

Graph Neural Point Process for Temporal Interaction Prediction

Temporal graphs are ubiquitous data structures in many scenarios, including social networks, user-item interaction networks, etc. In this paper, we focus on predicting the exact time of the next interaction, given a node pair on a temporal graph. This novel problem can support interesting applications, such as time-sensitive items recommendation, congestion prediction on road networks, and many others. We present Graph Neural Point Process (GNPP) to tackle this problem. GNPP relies on the graph neural message passing and the temporal point process framework. Most previous graph neural models only utilize the chronological order of observed events and ignore exact timestamps. In GNPP, we adapt a time encoding scheme to map real-valued timestamps to a high-dimensional vector space so that the temporal information can be precisely captured. Further, GNPP considers the structural information of graphs by conducting message-passing aggregation. The obtained representation defines a conditional intensity function that models events' generation mechanisms to predict future event times. We evaluate this model on synthetic and real-world datasets where it outperforms some recently proposed neural point process models and GNNs. We further conduct ablation comparisons and visualizations to shed some light on the learned model and understand the functionality of important components.

New Upper Bound and Lower Bound for Degree-Based Network Entropy

The degree-based network entropy which is inspired by Shannon’s entropy concept becomes the information-theoretic quantity for measuring the structural information of graphs and complex networks. In this paper, we study some properties of the degree-based network entropy. Firstly we develop a refinement of Jensen’s inequality. Next we present the new and more accurate upper bound and lower bound for the degree-based network entropy only using the order, the size, the maximum degree and minimum degree of a network. The bounds have desirable performance to restrict the entropy in different kinds of graphs. Finally, we show an application to structural complexity analysis of a computer network modeled by a connected graph.