We present a probabilistic generative model and efficient algorithm to model reciprocity in directed networks. Unlike other methods that address this problem such as exponential random graphs, it assigns latent variables as community memberships to nodes and a reciprocity parameter to the whole network rather than fitting order statistics. It formalizes the assumption that a directed interaction is more likely to occur if an individual has already observed an interaction towards her. It provides a natural framework for relaxing the common assumption in network generative models of conditional independence between edges, and it can be used to perform inference tasks such as predicting the existence of an edge given the observation of an edge in the reverse direction. Inference is performed using an efficient expectation-maximization algorithm that exploits the sparsity of the network, leading to an efficient and scalable implementation. We illustrate these findings by analyzing synthetic and real data, including social networks, academic citations and the Erasmus student exchange program. Our method outperforms others in both predicting edges and generating networks that reflect the reciprocity values observed in real data, while at the same time inferring an underlying community structure. We provide an open-source implementation of the code online.
To unravel the driving patterns of networks, the most popular models rely on community detection algorithms. However, these approaches are generally unable to reproduce the structural features of the network. Therefore, attempts are always made to develop models that incorporate these network properties beside the community structure. In this work, we present a probabilistic generative model and an efficient algorithm to both perform community detection and capture reciprocity in networks. Our approach jointly models pairs of edges with exact 2-edge joint distributions. In addition, it provide…
Building on existing stochastic actor-oriented models for panel data, we employ a conditional logistic framework to explore growth mechanisms for tie creation in continuously-observed networks. This framework models the likelihood of tie formation distinguishing it from hazard models that consider time to tie formation. It enables multiple growth mechanisms for network evolution (homophily, focus constraints, reinforcement, reciprocity, triadic closure, and popularity) to be modeled simultaneously. We apply this framework to communication within a Facebook-like community. The findings exemplif…
Network data is ubiquitous and growing, yet we lack realistic generative network models that can be calibrated to match real-world data. The recently proposed Block Two-Level Erdss-Renyi (BTER) model can be tuned to capture two fundamental properties: degree distribution and clustering coefficients. The latter is particularly important for reproducing graphs with community structure, such as social networks. In this paper, we compare BTER to other scalable models and show that it gives a better fit to real data. We provide a scalable implementation that requires only O(d_max) storage where d_m…
Reciprocity is a vital feature of social networks, but relatively little is known about its temporal structure or the mechanisms underlying its persistence in real world behavior. In pursuit of these two questions, we study the stationary and dynamical signals of reciprocity in a network of manioc beer (Spanish: chicha; Tsimane': shocdye') drinking events in a Tsimane' village in lowland Bolivia. At the stationary level, our analysis reveals that social exchange within the community is heterogeneously patterned according to kinship and spatial proximity. A positive relationship between the fre…
Weaker Coherence, Weaker Reciprocity: Comparing the Semantic and Social Organization of Moltbook and Reddit
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales（布宜诺斯艾利斯大学，理学院）；Instituto de Física Interdisciplinaria y Aplicada (INFINA), CONICET – Universidad de Buenos Aires（跨学科与应用物理研究所 (INFINA)，阿根廷国家科学研究委员会 - 布宜诺斯艾利斯大学）；Instituto Balseiro, Universidad Nacional de Cuyo y Comisión Nacional de Energía Atómica（巴尔塞罗研究所，门多萨国立大学与阿根廷国家原子能委员会）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（阿根廷国家科学研究委员会 (CONICET)）
Local network community detection aims to find a single community in a large network, while inspecting only a small part of that network around a given seed node. This is much cheaper than finding all communities in a network. Most methods for local community detection are formulated as ad-hoc optimization problems. In this work, we instead start from a generative model for networks with community structure. By assuming that the network is uniform, we can approximate the structure of unobserved parts of the network to obtain a method for local community detection. We apply this local approxima…
Community detection emerges as an important task in the discovery of network mesoscopic structures. However, the concept of a "good" community is very context-dependent and it is relatively complicated to deduce community characteristics using available community detection techniques. In reality, the existence of a gap between structural goodness quality metrics and expected topological patterns creates a confusion in evaluating community structures. In this paper, we introduce an empirical multivariate analysis of different structural goodness properties in order to characterize several detec…
Community detection refers to the task of discovering groups of vertices sharing similar properties or functions so as to understand the network data. With the recent development of deep learning, graph representation learning techniques are also utilized for community detection. However, the communities can only be inferred by applying clustering algorithms based on learned vertex embeddings. These general cluster algorithms like K-means and Gaussian Mixture Model cannot output much overlapped communities, which have been proved to be very common in many real-world networks. In this paper, we…
Many real-world networks known as attributed networks contain two types of information: topology information and node attributes. It is a challenging task on how to use these two types of information to explore structural regularities. In this paper, by characterizing potential relationship between link communities and node attributes, a principled statistical model named PSB_PG that generates link topology and node attributes is proposed. This model for generating links is based on the stochastic blockmodels following a Poisson distribution. Therefore, it is capable of detecting a wide range …
Michigan State University（密歇根州立大学）；NEC Laboratories America（美国 NEC 实验室）
This paper addresses the problem of community detection in networked data that combines link and content analysis. Most existing work combines link and content information by a generative model. There are two major shortcomings with the existing approaches. First, they assume that the probability of creating a link between two nodes is determined only by the community memberships of the nodes; however other factors (e.g. popularity) could also affect the link pattern. Second, they use generative models to model the content of individual nodes, whereas these generative models are vulnerable to …
Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there are node features in real networks, such as gender types in social networks, feeding behavior in ecological networks, and location on e-trading networks, that can be further leveraged with the network structure to attain more accurate community detection methods. We propose a novel probabilistic graphical model to detect communities by taking into account bo…
National Taiwan University（台湾大学）；Mila-Quebec Institute for Learning Algorithms（Mila-魁北克学习算法研究所）；Harvard University（哈佛大学）；Element AI；HEC Montreal（蒙特利尔高等商学院）
This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both…
The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph is inconsistent with the underlying model. The latter is model-free but fails to provide quality assurance for the detected communities. In this paper, we propose a novel unified framework to combine the advantages of these two principles. The presented method, SGC-GEN, not only considers the detection error caused by the corresponding model mi…
We propose a generative model to detect globally optimal community structures in networks by utilizing random walks. Sophisticated parameter optimization algorithms are developed based on the Markov chain Monte Carlo methods to overcome limitations of the EM algorithm, which has been used in previous works but is sometimes trapped in local optima depending on initial conditions. We apply the algorithms to synthetic and real-world networks to examine their performance in terms of precision and robustness of detected communities. It is found that the Gibbs samplers outperform the previous approa…
Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This paper is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or two-mode networks. We propose two generative models that can be easily tuned to reproduce the characteristics of real-world networks, not just qualitatively, but quantitatively. The characteristics we consider are the degree distributions and the metamorphosis coefficient. The metamorphosis coefficient, a bipartite analogue of the clustering coefficient, is the pro…
Graph sparsification aims to reduce the number of edges of a network while maintaining its accuracy for given tasks. In this study, we propose a novel method called GSGAN, which is able to sparsify networks for community detection tasks. GSGAN is able to capture those relationships that are not shown in the original graph but are relatively important, and creating artificial edges to reflect these relationships and further increase the effectiveness of the community detection task. We adopt GAN as the learning model and guide the generator to produce random walks that are able to capture the s…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric interactions are still not well developed and are unable to reproduce several basic topological properties. This is particularly disconcerting considering that real directed networks are the norm rather than the exception in many natural and human-made complex systems. In this paper, we fill this gap and show how the network geometry paradigm can be elegantly extended…
Assessing the partitioning performance of community detection algorithms is one of the most important issues in complex network analysis. Artificially generated networks are often used as benchmarks for this purpose. However, previous studies showed their level of realism have a significant effect on the algorithms performance. In this study, we adopt a thorough experimental approach to tackle this problem and investigate this effect. To assess the level of realism, we use consensual network topological properties. Based on the LFR method, the most realistic generative method to date, we propo…
Cooperation is a major factor in the evolution of human societies. The structure of human social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these signatures is the tendency to organize as groups. Among the generative models that network theorists use to emulate this feature is the Stochastic Block Model (SBM). In this paper, we study evolutionary game dynamics on SBM networks. Using a recently-discovered duality between evolutionary games and coalescing random walks, we obtain analytical conditions such that …
Communities in social networks or graphs are sets of well-connected, overlapping vertices. The effectiveness of a community detection algorithm is determined by accuracy in finding the ground-truth communities and ability to scale with the size of the data. In this work, we provide three contributions. First, we show that a popular measure of accuracy known as the F1 score, which is between 0 and 1, with 1 being perfect detection, has an information lower bound is 0.5. We provide a trivial algorithm that produces communities with an F1 score of 0.5 for any graph! Somewhat surprisingly, we find…
University of Toledo（托莱多大学）；The Ohio State University（俄亥俄州立大学）
The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node p…
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block model or planted partition problem, where a phase transition takes place in the detection of the planted partition by changing the signal-to-noise ratio. Optimal algorithms for the detection exist which are based on spectral methods, but we show these are extremely sensible to slight modification in the generative model. Recently Javanmard, Montanari and Ricci-T…
Dankook University（檀国大学）；Yonsei University（延世大学）；University of Konstanz（康斯坦茨大学）
The discovery of community structures in social networks has gained significant attention since it is a fundamental problem in understanding the networks' topology and functions. However, most social network data are collected from partially observable networks with both missing nodes and edges. In this paper, we address a new problem of detecting overlapping community structures in the context of such an incomplete network, where communities in the network are allowed to overlap since nodes belong to multiple communities at once. To solve this problem, we introduce KroMFac, a new framework th…
Network homophily, the tendency of similar nodes to be connected, and transitivity, the tendency of two nodes being connected if they share a common neighbor, are conflated properties in network analysis, since one mechanism can drive the other. Here we present a generative model and corresponding inference procedure that are capable of distinguishing between both mechanisms. Our approach is based on a variation of the stochastic block model (SBM) with the addition of triadic closure edges, and its inference can identify the most plausible mechanism responsible for the existence of every edge …
University of Colorado（科罗拉多大学）；BioFrontiers Institute（生物前沿研究所）
In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in…
Recent years have witnessed a growing number of researches on community characterization. In contrast to the large body of researches on the categorical measures (rise or decline) for evaluating the community development, we propose to estimate the community development strength (to which degree the rise or decline is). More specifically, given already known categorical information of community development, we are attempting to quantify the community development strength, which is of great interest. Motivated by the increasing availability of large-scale data on the network between entities am…
We consider the canonical problem of influence maximization in social networks. Since the seminal work of Kempe, Kleinberg, and Tardos, there have been two largely disjoint efforts on this problem. The first studies the problem associated with learning the parameters of the generative influence model. The second focuses on the algorithmic challenge of identifying a set of influencers, assuming the parameters of the generative model are known. Recent results on learning and optimization imply that in general, if the generative model is not known but rather learned from training data, no algorit…
Analyzing the groups in the network based on same attributes, functions or connections between nodes is a way to understand network information. The task of discovering a series of node groups is called community detection. Generally, two types of information can be utilized to fulfill this task, i.e., the link structures and the node attributes. The temporal text network is a special kind of network that contains both sources of information. Typical representatives include online blog networks, the World Wide Web (WWW) and academic citation networks. In this paper, we study the problem of ove…
The clustering ensemble paradigm has emerged as an effective tool for community detection in multilayer networks, which allows for producing consensus solutions that are designed to be more robust to the algorithmic selection and configuration bias. However, one limitation is related to the dependency on a co-association threshold that controls the degree of consensus in the community structure solution. The goal of this work is to overcome this limitation with a new framework of ensemble-based multilayer community detection, which features parameter-free identification of consensus communitie…
Huawei Noah's Ark Lab（华为诺亚方舟实验室）；University of South Florida（南佛罗里达大学）；University of Michigan（密歇根大学）；GIPSA-lab, University Grenoble-Alpes（格勒诺布尔-阿尔卑斯大学GIPSA实验室）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院MIT-IBM沃森人工智能实验室）
We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to follow a generative probabilistic model that takes into account the similarities and dissimilarities between the communities. We make use of a variational Bayes approach for jointly inferring the shared and unshared hidden communities from multilayer network observations. We show that our approach outperforms state-of-the-art algorithms in detecting disparate (shared and private) communities on synthetic data as well…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical model for such networks (called dynamic networks). We consider the case where the number of nodes is fixed, but the presence of edges can vary over time. Our model allows the number of communities in the network to be different at different time steps. We use a neural network based methodology to perform approximate inference in the proposed model and its simp…
