On Graph Stream Clustering with Side Information

Graph clustering becomes an important problem due to emerging applications involving the web, social networks and bio-informatics. Recently, many such applications generate data in the form of streams. Clustering massive, dynamic graph streams is significantly challenging because of the complex structures of graphs and computational difficulties of continuous data. Meanwhile, a large volume of side information is associated with graphs, which can be of various types. The examples include the properties of users in social network activities, the meta attributes associated with web click graph streams and the location information in mobile communication networks. Such attributes contain extremely useful information and has the potential to improve the clustering process, but are neglected by most recent graph stream mining techniques. In this paper, we define a unified distance measure on both link structures and side attributes for clustering. In addition, we propose a novel optimization framework DMO, which can dynamically optimize the distance metric and make it adapt to the newly received stream data. We further introduce a carefully designed statistics SGS(C) which consume constant storage spaces with the progression of streams. We demonstrate that the statistics maintained are sufficient for the clustering process as well as the distance optimization and can be scalable to massive graphs with side attributes. We will present experiment results to show the advantages of the approach in graph stream clustering with both links and side information over the baselines.Comment: Full version of SIAM SDM 2013 pape

Communication-Optimal Distributed Dynamic Graph Clustering

We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed distributively. We propose communication-efficient algorithms for two well-established communication models namely the message passing and the blackboard models. Given a graph with $n$ nodes that is observed at $s$ remote sites over time $[1,t]$, the two proposed algorithms have communication costs $\tilde{O}(ns)$ and $\tilde{O}(n+s)$ ($\tilde{O}$ hides a polylogarithmic factor), almost matching their lower bounds, $\Omega(ns)$ and $\Omega(n+s)$, respectively, in the message passing and the blackboard models. More importantly, we prove that at each time point in $[1,t]$ our algorithms generate clustering quality nearly as good as that of centralizing all updates up to that time and then applying a standard centralized clustering algorithm. We conducted extensive experiments on both synthetic and real-life datasets which confirmed the communication efficiency of our approach over baseline algorithms while achieving comparable clustering results.Comment: Accepted and to appear in AAAI'1

Graph-Level Embedding for Time-Evolving Graphs

Graph representation learning (also known as network embedding) has been extensively researched with varying levels of granularity, ranging from nodes to graphs. While most prior work in this area focuses on node-level representation, limited research has been conducted on graph-level embedding, particularly for dynamic or temporal networks. However, learning low-dimensional graph-level representations for dynamic networks is critical for various downstream graph retrieval tasks such as temporal graph similarity ranking, temporal graph isomorphism, and anomaly detection. In this paper, we present a novel method for temporal graph-level embedding that addresses this gap. Our approach involves constructing a multilayer graph and using a modified random walk with temporal backtracking to generate temporal contexts for the graph's nodes. We then train a "document-level" language model on these contexts to generate graph-level embeddings. We evaluate our proposed model on five publicly available datasets for the task of temporal graph similarity ranking, and our model outperforms baseline methods. Our experimental results demonstrate the effectiveness of our method in generating graph-level embeddings for dynamic networks.Comment: In Companion Proceedings of the ACM Web Conference 202

LLM4DyG: Can Large Language Models Solve Problems on Dynamic Graphs?

In an era marked by the increasing adoption of Large Language Models (LLMs) for various tasks, there is a growing focus on exploring LLMs' capabilities in handling web data, particularly graph data. Dynamic graphs, which capture temporal network evolution patterns, are ubiquitous in real-world web data. Evaluating LLMs' competence in understanding spatial-temporal information on dynamic graphs is essential for their adoption in web applications, which remains unexplored in the literature. In this paper, we bridge the gap via proposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic graphs, to the best of our knowledge, for the first time. Specifically, we propose the LLM4DyG benchmark, which includes nine specially designed tasks considering the capability evaluation of LLMs from both temporal and spatial dimensions. Then, we conduct extensive experiments to analyze the impacts of different data generators, data statistics, prompting techniques, and LLMs on the model performance. Finally, we propose Disentangled Spatial-Temporal Thoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal understanding abilities. Our main observations are: 1) LLMs have preliminary spatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph tasks show increasing difficulties for LLMs as the graph size and density increase, while not sensitive to the time span and data generation mechanism, 3) the proposed DST2 prompting method can help to improve LLMs' spatial-temporal understanding abilities on dynamic graphs for most tasks. The data and codes will be open-sourced at publication time

DYMOND: DYnamic MOtif-NoDes Network Generative Model

Motifs, which have been established as building blocks for network structure, move beyond pair-wise connections to capture longer-range correlations in connections and activity. In spite of this, there are few generative graph models that consider higher-order network structures and even fewer that focus on using motifs in models of dynamic graphs. Most existing generative models for temporal graphs strictly grow the networks via edge addition, and the models are evaluated using static graph structure metrics -- which do not adequately capture the temporal behavior of the network. To address these issues, in this work we propose DYnamic MOtif-NoDes (DYMOND) -- a generative model that considers (i) the dynamic changes in overall graph structure using temporal motif activity and (ii) the roles nodes play in motifs (e.g., one node plays the hub role in a wedge, while the remaining two act as spokes). We compare DYMOND to three dynamic graph generative model baselines on real-world networks and show that DYMOND performs better at generating graph structure and node behavior similar to the observed network. We also propose a new methodology to adapt graph structure metrics to better evaluate the temporal aspect of the network. These metrics take into account the changes in overall graph structure and the individual nodes' behavior over time.Comment: In Proceedings of the Web Conference 2021 (WWW '21

Google matrix of business process management

Development of efficient business process models and determination of their characteristic properties are subject of intense interdisciplinary research. Here, we consider a business process model as a directed graph. Its nodes correspond to the units identified by the modeler and the link direction indicates the causal dependencies between units. It is of primary interest to obtain the stationary flow on such a directed graph, which corresponds to the steady-state of a firm during the business process. Following the ideas developed recently for the World Wide Web, we construct the Google matrix for our business process model and analyze its spectral properties. The importance of nodes is characterized by Page-Rank and recently proposed CheiRank and 2DRank, respectively. The results show that this two-dimensional ranking gives a significant information about the influence and communication properties of business model units. We argue that the Google matrix method, described here, provides a new efficient tool helping companies to make their decisions on how to evolve in the exceedingly dynamic global market.Comment: submitted to European Journal of Physics