While language models (LMs) have demonstrated remarkable general-purpose capabilities across domains, including molecule generation using line notations such as SMILES and SELFIES, their direct application to 3D structure design remains constrained by two interdependent challenges. First, the difficulty in designing a 3D line notation that ensures SE(3)-invariant atomic coordinates and supports autoregressive generation. Second, the incompatibility between continuous spatial coordinates and the discrete token inputs required by LMs. To address this, we propose Mol-StrucTok, a unified framework for tokenizing 3D molecular structures. Our approach comprises two key innovations: (1) a 3D line notation—Spherical Coordinate Notation—that encodes local atomic environments in spherical coordinates, agnostic to 2D notations and inherently SE(3)-invariant; and (2) a structure-aware Vector Quantized Variational Autoencoder (VQ-VAE) for discretizing these coordinates into chemically valid tokens suitable for language model processing. Leveraging this tokenization framework, we train a GPT-2 style model for end-to-end 3D molecular generation. Empirical results demonstrate strong, task-dependent performance: in unconditional generation, Mol-StrucTok achieves diffusion-level stability with ~28× faster inference; in conditional generation, it reduces property-matching mean absolute error (MAE) by 5–8× compared to diffusion-based methods, highlighting the advantage of autoregressive contextual modeling for precise control of molecular attributes. Our code is available at https://github.com/KyGao/Mol-StrucTok.

Much of the complexity of social, biological, and engineering systems arises from the complicated interactions among the entities in the corresponding networks. A number of network analysis tools have been successfully used to discover latent structures termed communities in such networks. However, some communities with relatively weak structures can be difficult to uncover because they are obscured by other stronger connections. To cope with this situation, our previous work proposes an algorithm called HICODE to detect and amplify the dominant and hidden community structures. In this work, we conduct a comprehensive and systematic theoretical analysis on the impact of hidden community structure and the efficacy of the HICODE algorithm, as well as provide illustrations of the detection process and results. Specifically, we define a multi-layer stochastic block model and use this model to explain why the existence of hidden structure makes the detection of dominant structure harder than equivalent random noises, which can also explain why many community detection algorithms only focusing on the dominant structure do not work well as expected. We then provide theoretical analysis that the iterative reducing methods could help to enhance the discovery of hidden structure as well as the dominant structure in the multi-layer stochastic block model for the two cases of accurate and inaccurate detection. Finally, visual simulations and experimental results are presented to show the process of HICODE algorithm and the impact of different number of layers on the detection quality.

Hidden community is a useful concept proposed recently for social network analysis. Hidden communities indicate some weak communities whose most members also belong to other stronger dominant communities. Dominant communities could form a layer that partitions all the individuals of a network, and hidden communities could form other layer(s) underneath. These layers could be natural structures in the real-world networks like students grouped by major, minor, hometown, and so on. To handle the rapid growth of network scale, in this work, we explore the detection of hidden communities from the local perspective, and propose a new method that detects and boosts each layer iteratively on a subgraph sampled from the original network. We first expand the seed set from a single seed node based on our modified local spectral method and detect an initial dominant local community. Then we temporarily remove the members of this community as well as their connections to other nodes, and detect all the neighborhood communities in the remaining subgraph, including some “broken communities” that only contain a fraction of members in the original network. The local community and neighborhood communities form a dominant layer, and by reducing the edge weights inside these communities, we weaken this layer’s structure to reveal the hidden layers. Eventually, we repeat the whole process, and all communities containing the seed node can be detected and boosted iteratively. We theoretically show that our method can avoid some situations that a broken community and the local community are regarded as one community in the subgraph, leading to the inaccuracy of detection which can be caused by global hidden community detection methods. Extensive experiments show that our method could significantly outperform the state-of-the-art baselines designed for either global hidden community detection or multiple local community detection.

In this paper we make progress on the unsupervised task of mining arbitrarily shaped clusters in highly noisy datasets, which is a task present in many real-world applications. Based on the fundamental work that first applies a wavelet transform to data clustering, we propose an adaptive clustering algorithm, denoted as AdaWave, which exhibits favorable characteristics for clustering. By a self-adaptive thresholding technique, AdaWave is parameter free and can handle data in various situations. It is deterministic, fast in linear time, order-insensitive, shape-insensitive, robust to highly noisy data, and requires no pre-knowledge on data models. Moreover, AdaWave inherits the ability from the wavelet transform to cluster data in different resolutions. We adopt the "grid labeling" data structure to drastically reduce the memory consumption of the wavelet transform so that AdaWave can be used for relatively high dimensional data. Experiments on synthetic as well as natural datasets demonstrate the effectiveness and efficiency of our proposed method.

Community detection is an important information mining task to uncover modular structures in large networks. For increasingly common large network datasets, global community detection is prohibitively expensive, and attention has shifted to methods that mine local communities, i.e., identifying all latent members of a particular community from a few labeled seed members. To address such semi-supervised mining task, we systematically develop a local spectral (LOSP) subspace-based community detection method, called LOSP. We define a family of LOSP subspaces based on Krylov subspaces, and seek a sparse indicator for the target community via an ℓ 1 norm minimization over the Krylov subspace. Variants of LOSP depend on type of random walks with different diffusion speeds, type of random walks, dimension of the LOSP subspace, and step of diffusions. The effectiveness of the proposed LOSP approach is theoretically analyzed based on Rayleigh quotients, and it is experimentally verified on a wide variety of real-world networks across social, production, and biological domains, as well as on an extensive set of synthetic LFR benchmark datasets.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms for mining communities have focused on global graph structure, and often run in time proportional to the size of the entire graph. As we explore networks with millions of vertices and find communities of size in the hundreds, it becomes important to shift our attention from macroscopic structure to microscopic structure in large networks. A growing body of work has been adopting local expansion methods in order to identify communities from a few exemplary seed members. In this article, we propose a novel approach for finding overlapping communities called L emon ( L ocal E xpansion via M inimum O ne N orm). Provided with a few known seeds , the algorithm finds the community by performing a local spectral diffusion. The core idea of L emon is to use short random walks to approximate an invariant subspace near a seed set, which we refer to as local spectra . Local spectra can be viewed as the low-dimensional embedding that captures the nodes’ closeness in the local network structure. We show that L emon ’s performance in detecting communities is competitive with state-of-the-art methods. Moreover, the running time scales with the size of the community rather than that of the entire graph. The algorithm is easy to implement and is highly parallelizable. We further provide theoretical analysis of the local spectral properties, bounding the measure of tightness of extracted community using the eigenvalues of graph Laplacian. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the seed set quality and quantity would affect the performance are provided.

How can web services that depend on user generated content discern fake social engagement activities by spammers from legitimate ones? In this paper, we focus on the social site of YouTube and the problem of identifying bad actors posting inorganic contents and inflating the count of social engagement metrics. We propose an effective method, Leas (Local Expansion at Scale), and show how the fake engagement activities on YouTube can be tracked over time by analyzing the temporal graph based on the engagement behavior pattern between users and YouTube videos. With the domain knowledge of spammer seeds, we formulate and tackle the problem in a semi-supervised manner --- with the objective of searching for individuals that have similar pattern of behavior as the known seeds --- based on a graph diffusion process via local spectral subspace. We offer a fast, scalable MapReduce deployment adapted from the localized spectral clustering algorithm. We demonstrate the effectiveness of our deployment at Google by achieving a manual review accuracy of 98% on YouTube Comments graph in practice. Comparing with the state-of-the-art algorithm CopyCatch, Leas achieves 10 times faster running time on average. Leas is now actively in use at Google, searching for daily deceptive practices on YouTube's engagement graph spanning over a billion users.

Social instant messaging services are emerging as a transformative form with which people connect, communicate with friends in their daily life they catalyze the formation of social groups, and they bring people stronger sense of community and connection. However, research community still knows little about the formation and evolution of groups in the context of social messaging their lifecycles, the change in their underlying structures over time, and the diffusion processes by which they develop new members. In this paper, we analyze the daily usage logs from WeChat group messaging platform the largest standalone messaging communication service in China with the goal of understanding the processes by which social messaging groups come together, grow new members, and evolve over time. Specifically, we discover a strong dichotomy among groups in terms of their lifecycle, and develop a separability model by taking into account a broad range of group-level features, showing that long-term and short-term groups are inherently distinct. We also found that the lifecycle of messaging groups is largely dependent on their social roles and functions in users' daily social experiences and specific purposes. Given the strong separability between the long-term and short-term groups, we further address the problem concerning the early prediction of successful communities. In addition to modeling the growth and evolution from group-level perspective, we investigate the individual-level attributes of group members and study the diffusion process by which groups gain new members. By considering members' historical engagement behavior as well as the local social network structure that they embedded in, we develop a membership cascade model and demonstrate the effectiveness by achieving AUC of 95.31% in predicting inviter, and an AUC of 98.66% in predicting invitee.

Based on the definition of local spectral subspace, we propose a novel approach called LOSP for local overlapping community detection. Using the power method for a few steps, LOSP finds an approximate invariant subspace, which depicts the embedding of the local neighborhood structure around the seeds of interest. LOSP then identifies the local community expanded from the given seeds by seeking a sparse indicator vector in the subspace where the seeds are in its support. We provide a systematic investigation on LOSP, and thoroughly evaluate it on large real world networks across multiple domains. With the prior information of very few seed members, LOSP can detect the remaining members of a target community with high accuracy. Experiments demonstrate that LOSP outperforms the Heat Kernel and PageRank diffusions. Using LOSP as a subroutine, we further address the problem of multiple membership identification, which aims to find all the communities a single vertex belongs to. High F1 scores are achieved in detecting multiple local communities with respect to arbitrary single seed for various large real world networks.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify the community from a few exemplary seed members. %Very few approaches can systematically demonstrate both high efficiency and effectiveness that significantly stands out amongst the divergent approaches in finding communities.

The recent interest in networks has inspired a broad range of work on algorithms and techniques to characterize, identify, and extract communities from networks. Such efforts are complicated by a lack of consensus on what a “community” truly is, and these disagreements have led to a wide variety of mathematical formulations for describing communities. Often, these mathematical formulations, such as modularity and conductance, have been founded in the general principle that communities, like a G ( n , p ) graph, are “round,” with connections throughout the entire community, and so algorithms were developed to optimize such mathematical measures. More recently, a variety of algorithms have been developed that, rather than expecting connectivity through the entire community, seek out very small groups of well-connected nodes and then connect these groups into larger communities. In this article, we examine seven real networks, each containing external annotation that allows us to identify “annotated communities.” A study of these annotated communities gives insight into why the second category of community detection algorithms may be more successful than the first category. We then present a flexible algorithm template that is based on the idea of joining together small sets of nodes. In this template, we first identify very small, tightly connected “subcommunities” of nodes, each corresponding to a single node’s “perception” of the network around it. We then create a new network in which each node represents such a subcommunity, and then identify communities in this new network. Because each node can appear in multiple subcommunities, this method allows us to detect overlapping communities. When evaluated on real data, we show that our template outperforms many other state-of-the-art algorithms.

Four major factors govern the intricacies of community extraction in networks: (1) the literature offers a multitude of disparate community detection algorithms whose output exhibits high structural variability across the collection, (2) communities identified by algorithms may differ structurally from real communities that arise in practice, (3) there is no consensus characterizing how to discriminate communities from noncommunities, and (4) the application domain includes a wide variety of networks of fundamentally different natures. In this article, we present a class separability framework to tackle these challenges through a comprehensive analysis of community properties. Our approach enables the assessment of the structural dissimilarity among the output of multiple community detection algorithms and between the output of algorithms and communities that arise in practice. In addition, our method provides us with a way to organize the vast collection of community detection algorithms by grouping those that behave similarly. Finally, we identify the most discriminative graph-theoretical properties of community signature and the small subset of properties that account for most of the biases of the different community detection algorithms. We illustrate our approach with an experimental analysis, which reveals nuances of the structure of real and extracted communities. In our experiments, we furnish our framework with the output of 10 different community detection procedures, representative of categories of popular algorithms available in the literature, applied to a diverse collection of large-scale real network datasets whose domains span biology, online shopping, and social systems. We also analyze communities identified by annotations that accompany the data, which reflect exemplar communities in various domain. We characterize these communities using a broad spectrum of community properties to produce the different structural classes. As our experiments show that community structure is not a universal concept, our framework enables an informed choice of the most suitable community detection method for identifying communities of a specific type in a given network and allows for a comparison of existing community detection algorithms while guiding the design of new ones.

We study how links are formed in social networks. In particular, we focus on investigating how a reciprocal (two-way) link, the basic relationship in social networks, is developed from a parasocial (one-way) relationship and how the relationships further develop into triadic closure, one of the fundamental processes of link formation. We first investigate how geographic distance and interactions between users influence the formation of link structure among users. Then we study how social theories including homophily, social balance, and social status are satisfied over networks with parasocial and reciprocal relationships. The study unveils several interesting phenomena. For example, “friend's friend is a friend” indeed exists in the reciprocal relationship network, but does not hold in the parasocial relationship network. We propose a learning framework to formulate the problems of predicting reciprocity and triadic closure into a graphical model. We demonstrate that it is possible to accurately infer 90% of reciprocal relationships in a Twitter network. The proposed model also achieves better performance (+20--30% in terms of F1-measure) than several alternative methods for predicting the triadic closure formation.

Three major factors govern the intricacies of community extraction in networks: (1) the application domain includes a wide variety of networks of fundamentally different natures, (2) the literature offers a multitude of disparate community detection algorithms, and (3) there is no consensus characterizing how to discriminate communities from non-communities. In this paper, we present a comprehensive analysis of community properties through a class separability framework. Our approach enables the assessement of the structural dissimilarity among the output of multiple community detection algorithms and between the output of algorithms and communities that arise in practice. To demostrate this concept, we furnish our method with a large set of structural properties and multiple community detection algorithms. Applied to a diverse collection of large scale network datasets, the analysis reveals that (1) the different detection algorithms extract fundamentally different structures; (2) the structure of communities that arise in practice is closest to that of communities that random-walk-based algorithms extract, although still siginificantly different from that of the output of all the algorithms; and (3) a small subset of the properties are nearly as discriminative as the full set, while making explicit the ways in which the algorithms produce biases. Our framework enables an informed choice of the most suitable community detection method for a given purpose and network and allows for a comparison of existing community detection algorithms while guiding the design of new ones.

We study the extent to which the formation of a two-way relationship can be predicted in a dynamic social network. A two-way (called reciprocal) relationship, usually developed from a one-way (parasocial) relationship, represents a more trustful relationship between people. Understanding the formation of two-way relationships can provide us insights into the micro-level dynamics of the social network, such as what is the underlying community structure and how users influence each other. Employing Twitter as a source for our experimental data, we propose a learning framework to formulate the problem of reciprocal relationship prediction into a graphical model. The framework incorporates social theories into a machine learning model. We demonstrate that it is possible to accurately infer 90% of reciprocal relationships in a dynamic network. Our study provides strong evidence of the existence of the structural balance among reciprocal relationships. In addition, we have some interesting findings, e.g., the likelihood of two "elite" users creating a reciprocal relationships is nearly 8 times higher than the likelihood of two ordinary users. More importantly, our findings have potential implications such as how social structures can be inferred from individuals' behaviors.

In many social networks, there exist two types of users that exhibit different influence and different behavior. For instance, statistics have shown that less than 1% of the Twitter users (e.g. entertainers, politicians, writers) produce 50% of its content, while the others (e.g. fans, followers, readers) have much less influence and completely different social behavior. In this paper, we define and explore a novel problem called community kernel detection in order to uncover the hidden community structure in large social networks. We discover that influential users pay closer attention to those who are more similar to them, which leads to a natural partition into different community kernels. We propose Greedy and We BA, two efficient algorithms for finding community kernels in large social networks. Greedy is based on maximum cardinality search, while We BA formalizes the problem in an optimization framework. We conduct experiments on three large social networks: Twitter, Wikipedia, and Coauthor, which show that We BA achieves an average 15%-50% performance improvement over the other state-of-the-art algorithms, and We BA is on average 6-2,000 times faster in detecting community kernels.

In this paper we study how to discover the evolution of topics over time in a time-stamped document collection. Our approach is uniquely designed to capture the rich topology of topic evolution inherent in the corpus. Instead of characterizing the evolving topics at fixed time points, we conceptually define a topic as a quantized unit of evolutionary change in content and discover topics with the time of their appearance in the corpus. Discovered topics are then connected to form a topic evolution graph using a measure derived from the underlying document network. Our approach allows inhomogeneous distribution of topics over time and does not impose any topological restriction in topic evolution graphs. We evaluate our algorithm on the ACM corpus.

We are interested in finding natural communities in large-scale linked networks. Our ultimate goal is to track changes over time in such communities. For such temporal tracking, we require a clustering algorithm that is relatively stable under small perturbations of the input data. We have developed an efficient, scalable agglomerative strategy and applied it to the citation graph of the NEC CiteSeer database (250,000 papers; 4.5 million citations). Agglomerative clustering techniques are known to be unstable on data in which the community structure is not strong. We find that some communities are essentially random and thus unstable while others are natural and will appear in most clusterings. These natural communities will enable us to track the evolution of communities over time.