Recent years have witnessed a surge of interest in machine learning on graphs and networks with applications ranging from vehicular network design to IoT traffic management to social network recommendations. Supervised machine learning tasks in networks such as node classification and link prediction require us to perform feature engineering that is known and agreed to be the key to success in applied machine learning. Research efforts dedicated to representation learning, especially representation learning using deep learning, has shown us ways to automatically learn relevant features from vast amounts of potentially noisy, raw data. However, most of the methods are not adequate to handle heterogeneous information networks which pretty much represents most real-world data today. The methods cannot preserve the structure and semantic of multiple types of nodes and links well enough, capture higher-order heterogeneous connectivity patterns, and ensure coverage of nodes for which representations are generated. We propose a novel efficient algorithm, motif2vec that learns node representations or embeddings for heterogeneous networks. Specifically, we leverage higher-order, recurring, and statistically significant network connectivity patterns in the form of motifs to transform the original graph to motif graph(s), conduct biased random walk to efficiently explore higher order neighborhoods, and then employ heterogeneous skip-gram model to generate the embeddings. Unlike previous efforts that uses different graph meta-structures to guide the random walk, we use graph motifs to transform the original network and preserve the heterogeneity. We evaluate the proposed algorithm on multiple real-world networks from diverse domains and against existing state-of-the-art methods on multi-class node classification and link prediction tasks, and demonstrate its consistent superiority over prior work.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Heterogeneous information networks (HINs) with rich semantics are ubiquitous in real-world applications. For a given HIN, many reasonable clustering results with distinct semantic meaning can simultaneously exist. User-guided clustering is hence of great practical value for HINs where users provide labels to a small portion of nodes. To cater to a broad spectrum of user guidance evidenced by different expected clustering results, carefully exploiting the signals residing in the data is potentially useful. Meanwhile, as one type of complex networks, HINs often encapsulate higher-order interacti…
Dalian University of Technology（大连理工大学）；Federation University Australia（澳大利亚联邦大学）；University of South Australia（南澳大利亚大学）
Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly aims at accelerating and improving higher-order graph learning results. We apply the acceleration procedure from the dimensional of network motifs. Specifically, the refined degree for nodes and edges are conducted in two stages: (1) employ motif degree of nodes to refine the adjacency matrix of the network; and (2) employ motif degree of edges to refine the …
School of Mathematical Science, Beihang University（北京航空航天大学数学科学学院）；Key Laboratory of Mathematics Informatics Behavioral Semantics, Ministry of Education（教育部数学、信息与行为语义重点实验室）；Peng Cheng Laboratory（鹏城实验室）；Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University（北京航空航天大学大数据与脑机智能北京高精尖创新中心）
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction , etc. However, most of the existing approaches start from the binary relationship (i.e., edges) in the graph and have not leveraged the higher order local structure (i.e., motifs) of the graph. Here, we propose mGCMN -- a novel framework which utilizes node feature information and the higher order local structure of the graph to effectively generate node embed…
Ocean University of China（中国海洋大学）；Massachusetts Institute of Technology（麻省理工学院）；The University of Hong Kong（香港大学）
One fundamental problem in temporal graph analysis is to count the occurrences of small connected subgraph patterns (i.e., motifs), which benefits a broad range of real-world applications, such as anomaly detection, structure prediction, and network representation learning. However, existing works focused on exacting temporal motif are not scalable to large-scale temporal graph data, due to their heavy computational costs or inherent inadequacy of parallelism. In this work, we propose a scalable parallel framework for exactly counting temporal motifs in large-scale temporal graphs. We first ca…
In this paper, we study network representation learning for tripartite heterogeneous networks which learns node representation features for networks with three types of node entities. We argue that tripartite networks are common in real world applications, and the essential challenge of the representation learning is the heterogeneous relations between various node types and links in the network. To tackle the challenge, we develop a tripartite heterogeneous network embedding called TriNE. The method considers unique user-item-tag tripartite relationships, to build an objective function to mod…
Pre-training Graph Neural Networks (GNN) via self-supervised contrastive learning has recently drawn lots of attention. However, most existing works focus on node-level contrastive learning, which cannot capture global graph structure. The key challenge to conducting subgraph-level contrastive learning is to sample informative subgraphs that are semantically meaningful. To solve it, we propose to learn graph motifs, which are frequently-occurring subgraph patterns (e.g. functional groups of molecules), for better subgraph sampling. Our framework MotIf-driven Contrastive leaRning Of Graph repre…
Existing message passing neural networks for heterogeneous graphs rely on the concepts of meta-paths or meta-graphs due to the intrinsic nature of heterogeneous graphs. However, the meta-paths and meta-graphs need to be pre-configured before learning and are highly dependent on expert knowledge to construct them. To tackle this challenge, we propose a novel concept of meta-node for message passing that can learn enriched relational knowledge from complex heterogeneous graphs without any meta-paths and meta-graphs by explicitly modeling the relations among the same type of nodes. Unlike meta-pa…
Beijing University of Posts and Telecommunications（北京邮电大学）
Learning knowledge representation of scientific paper data is a problem to be solved, and how to learn the representation of paper nodes in scientific paper heterogeneous network is the core to solve this problem. This paper proposes an unsupervised cluster-level scientific paper heterogeneous graph node representation learning method (UCHL), aiming at obtaining the representation of nodes (authors, institutions, papers, etc.) in the heterogeneous graph of scientific papers. Based on the heterogeneous graph representation, this paper performs link prediction on the entire heterogeneous graph a…
University of Science and Technology of China（中国科学技术大学）；Tencent America（腾讯美国）
Predicting molecular properties with data-driven methods has drawn much attention in recent years. Particularly, Graph Neural Networks (GNNs) have demonstrated remarkable success in various molecular generation and prediction tasks. In cases where labeled data is scarce, GNNs can be pre-trained on unlabeled molecular data to first learn the general semantic and structural information before being fine-tuned for specific tasks. However, most existing self-supervised pre-training frameworks for GNNs only focus on node-level or graph-level tasks. These approaches cannot capture the rich informati…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present InfoMotif, a new semi-supervised, motif-regularized, learning framework over graphs. We overcome two key limitations of message passing in popular graph neural networks (GNNs): localization (a k-layer GNN cannot utilize features outside the k-hop neighborhood of the labeled training nodes) and over-smoothed (structurally indistinguishable) representations. We propose the concept of attributed structural roles of nodes based on their occurrence in different network motifs, independent of network proximity. Two nodes share attributed structural roles if they participate in topological…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to model the key properties of local connectivity and translation invariance, using high-order connection patterns or motifs. We develop a novel deep architecture Motif-CNN that employs an attention model to combine the features extracted from multiple patterns, thus effectively capturing high-order structural and feature information. Our experiments on semi-supe…
Georgia State University（佐治亚州立大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Graph Neural networks (GNNs) have recently become a powerful technique for many graph-related tasks including graph classification. Current GNN models apply different graph pooling methods that reduce the number of nodes and edges to learn the higher-order structure of the graph in a hierarchical way. All these methods primarily rely on the one-hop neighborhood. However, they do not consider the higher- order structure of the graph. In this work, we propose a multi-channel Motif-based Graph Pooling method named (MPool) captures the higher-order graph structure with motif and local and global g…
PageRank has been widely used to measure the authority or the influence of a user in social networks. However, conventional PageRank only makes use of edge-based relations, which represent first-order relations between two connected nodes. It ignores higher-order relations that may exist between nodes. In this paper, we propose a novel framework, motif-based PageRank (MPR), to incorporate higher-order relations into the conventional PageRank computation. Motifs are subgraphs consisting of a small number of nodes. We use motifs to capture higher-order relations between nodes in a network and in…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite, k-partite, signed, labeled graphs, among many others. In this work, we generalize the notion of network motifs to heterogeneous networks. In particular, small induced typed subgraphs called typed graphlets (heterogeneous network motifs) are introduced and shown to be the fundamental building blocks of complex heterogeneous networks. Typed graphlets are a power…
Heterogeneous Information Networks (HIN) has been widely used in recommender systems (RSs). In previous HIN-based RSs, meta-path is used to compute the similarity between users and items. However, existing meta-path based methods only consider first-order relations, ignoring higher-order relations among the nodes of \textit{same} type, captured by \textit{motifs}. In this paper, we propose to use motifs to capture higher-order relations among nodes of same type in a HIN and develop the motif-enhanced meta-path (MEMP) to combine motif-based higher-order relations with edge-based first-order rel…
Evolving temporal networks serve as the abstractions of many real-life dynamic systems, e.g., social network and e-commerce. The purpose of temporal network embedding is to map each node to a time-evolving low-dimension vector for downstream tasks, e.g., link prediction and node classification. The difficulty of temporal network embedding lies in how to utilize the topology and time information jointly to capture the evolution of a temporal network. In response to this challenge, we propose a temporal motif-preserving network embedding method with bicomponent neighbor aggregation, named TME-BN…
Higher-order proximity (HOP) is fundamental for most network embedding methods due to its significant effects on the quality of node embedding and performance on downstream network analysis tasks. Most existing HOP definitions are based on either homophily to place close and highly interconnected nodes tightly in embedding space or heterophily to place distant but structurally similar nodes together after embedding. In real-world networks, both can co-exist, and thus considering only one could limit the prediction performance and interpretability. However, there is no general and universal sol…
Banking fraud causes billion-dollar losses for banks worldwide. In fraud detection, graphs help understand complex transaction patterns and discovering new fraud schemes. This work explores graph patterns in a real-world transaction dataset by extracting and analyzing its network motifs. Since banking graphs are heterogeneous, we focus on heterogeneous network motifs. Additionally, we propose a novel network randomization process that generates valid banking graphs. From our exploratory analysis, we conclude that network motifs extract insightful and interpretable patterns.
Federation University Australia（澳大利亚联邦大学）；Dalian University of Technology（大连理工大学）；Swinburne University of Technology（斯威本科技大学）；Deakin University（迪肯大学）；University of South Australia（南澳大利亚大学）
Clustering a group of vertices in networks facilitates applications across different domains, such as social computing and Internet of Things. However, challenges arises for clustering networks with increased scale. This paper proposes a solution which consists of two motif clustering techniques: standard acceleration CHIEF-ST and approximate acceleration CHIEF-AP. Both algorithms first find the maximal k-edge-connected subgraphs within the target networks to lower the network scale, then employ higher-order motifs in clustering. In the first procedure, we propose to lower the network scale by…
Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the …
A determinant property of the structure of a biological network is the distribution of local connectivity patterns, i.e., network motifs. In this work, a method for creating directed, unweighted networks while promoting a certain combination of motifs is presented. This motif-based network algorithm starts with an empty graph and randomly connects the nodes by advancing or discouraging the formation of chosen motifs. The in- or out-degree distribution of the generated networks can be explicitly chosen. The algorithm is shown to perform well in producing networks with high occurrences of the ta…
Counting the frequencies of 3-, 4-, and 5-node undirected motifs (also know as graphlets) is widely used for understanding complex networks such as social and biology networks. However, it is a great challenge to compute these metrics for a large graph due to the intensive computation. Despite recent efforts to count triangles (i.e., 3-node undirected motif counting), little attention has been given to developing scalable tools that can be used to characterize 4- and 5-node motifs. In this paper, we develop computational efficient methods to sample and count 4- and 5- node undirected motifs. O…
Tenuous subgraph finding aims to detect a subgraph with few social interactions and weak relationships among nodes. Despite significant efforts have been made on this task, they are mostly carried out in view of graph-structured data. These methods depend on calculating the shortest path and need to enumerate all the paths between nodes, which suffer the combinatorial explosion. Moreover, they all lack the integration of neighborhood information. To this end, we propose a novel model named Graph Neural Network with Motif-aware for tenuous subgraph finding (GNNM), a neighborhood aggregation bas…
Local clustering aims to identify a cluster within a given graph that includes a designated seed node or a significant portion of a group of seed nodes. This cluster should be well-characterized, i.e., it has a high number of internal edges and a low number of external edges. In this work, we propose SOCIAL, a novel algorithm for local motif clustering which optimizes for motif conductance based on a local hypergraph model representation of the problem and an adapted version of the max-flow quotient-cut improvement algorithm (MQI). In our experiments with the triangle motif, SOCIAL produces lo…
Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attenti…
The lifestyles of urban dwellers could reveal important insights regarding the dynamics and complexity of cities. Despite growing research on analysis of lifestyle patterns in cities, little is known about the characteristics of people's lifestyles patterns at urban scale. This limitation is primarily due to challenges in characterizing lifestyle patterns when human movement data is aggregated to protect the privacy of users. In this study, we model cities based on aggregated human visitation data to construct a network of places. We then examine the subgraph signatures in the networks of plac…
Randomized experiments, or "A/B" tests, remain the gold standard for evaluating the causal effect of a policy intervention or product change. However, experimental settings, such as social networks, where users are interacting and influencing one another, may violate conventional assumptions of no interference for credible causal inference. Existing solutions to the network setting include accounting for the fraction or count of treated neighbors in a user's network, yet most current methods do not account for the local network structure beyond simply counting the number of neighbors. Our stud…
A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network. Counting of motifs in complex networks has been a well-studied problem in network analysis of various real-word graphs arising from the study of social networks and bioinformatics. In particular, the triangle counting problem has received much attention due to its significance in understanding the behavior of social networks. Similarly, subgraphs with more than 3 nodes have received much attention recently. While there have been successful methods developed on this problem, most of the existing algorithms are not scala…
Temporal graphs are structures which model relational data between entities that change over time. Due to the complex structure of data, mining statistically significant temporal subgraphs, also known as temporal motifs, is a challenging task. In this work, we present an efficient technique for extracting temporal motifs in temporal networks. Our method is based on the novel notion of egocentric temporal neighborhoods, namely multi-layer structures centered on an ego node. Each temporal layer of the structure consists of the first-order neighborhood of the ego node, and corresponding nodes in …
Online stores like Amazon and Ebay are growing by the day. Fewer people go to departmental stores as opposed to the convenience of purchasing from stores online. These stores may employ a number of techniques to advertise and recommend the appropriate product to the appropriate buyer profile. This article evaluates various 3-node and 4-node motifs occurring in such networks. Community structures are evaluated too.These results may provide interesting insights into user behavior and a better understanding of marketing techniques.
The mining of graphs in terms of their local substructure is a well-established methodology to analyze networks. It was hypothesized that motifs - subgraph patterns which appear significantly more often than expected at random - play a key role for the ability of a system to perform its task. Yet the framework commonly used for motif-detection averages over the local environments of all nodes. Therefore, it remains unclear whether motifs are overrepresented in the whole system or only in certain regions. In this contribution, we overcome this limitation by mining node-specific triad patterns. …
Network motifs are patterns of over-represented node interactions in a network which have been previously used as building blocks to understand various aspects of the social networks. In this paper, we use motif patterns to characterize the information diffusion process in social networks. We study the lifecycle of information cascades to understand what leads to saturation of growth in terms of cascade reshares, thereby resulting in expiration, an event we call ``diffusion inhibition''. In an attempt to understand what causes inhibition, we use motifs to dissect the network obtained from info…
Network motifs can capture basic interaction patterns and inform the functional properties of networks. However, real-world complex systems often have multiple types of relationships, which cannot be represented by a monolayer network. The multilayer nature of complex systems demands research on extending the notion of motifs to multilayer networks, thereby exploring the interaction patterns with a higher resolution. In this paper, we propose a formal definition of multilayer motifs, and analyse the occurrence of three-node multilayer motifs in a set of real-world multilayer networks. We find …
The problem of calculating the frequencies of network motifs on three and four nodes in large networks is considered. Telecommunications networks, cell molecular networks are investigated. The sizes of the investigated networks are hundreds of thousands of nodes and connections. These networks are represented in the form of directed and undirected simple graphs. Exact calculating requires huge computational resources for such large graphs. A method for calculating the frequencies of network motifs using the Monte Carlo method with control of the accuracy of calculations is proposed. The propos…
College of Science and Engineering, HBKU（哈马德·本·哈利法大学科学与工程学院）；ISI Foundation（ISI基金会）；Qatar Computing Research Institute, HBKU（哈马德·本·哈利法大学卡塔尔计算研究所）
Link prediction requires predicting which new links are likely to appear in a graph. Being able to predict unseen links with good accuracy has important applications in several domains such as social media, security, transportation, and recommendation systems. A common approach is to use features based on the common neighbors of an unconnected pair of nodes to predict whether the pair will form a link in the future. In this paper, we present an approach for link prediction that relies on higher-order analysis of the graph topology, well beyond common neighbors. We treat the link prediction pro…
Institute for Theoretical Physics, University of Würzburg（维尔茨堡大学理论物理研究所）
The detection of triadic subgraph motifs is a common methodology in complex-networks research. The procedure usually applied in order to detect motifs evaluates whether a certain subgraph pattern is overrepresented in a network as a whole. However, motifs do not necessarily appear frequently in every region of a graph. For this reason, we recently introduced the framework of Node-Specific Pattern Mining (NoSPaM). This work is a manual for an implementation of NoSPaM which can be downloaded from www.mwinkler.eu.
Dense regions in networks are an indicator of interesting and unusual information. However, most existing methods only consider simple, undirected, unweighted networks. Complex networks in the real-world often have rich information though: edges are asymmetrical and nodes/edges have categorical and numerical attributes. Finding dense subgraphs in such networks in accordance with this rich information is an important problem with many applications. Furthermore, most existing algorithms ignore the higher-order relationships (i.e., motifs) among the nodes. Motifs are shown to be helpful for dense…
A widely-used operation on graphs is local clustering, i.e., extracting a well-characterized community around a seed node without the need to process the whole graph. Recently local motif clustering has been proposed: it looks for a local cluster based on the distribution of motifs. Since this local clustering perspective is relatively new, most approaches proposed for it are extensions of statistical and numerical methods previously used for edge-based local clustering, while the available combinatorial approaches are still few and relatively simple. In this work, we build a hypergraph and a …
How does the small-scale topological structure of an airline network behave as the network evolves? To address this question, we study the dynamic properties of small undirected subgraphs using 15 years of data on Southwest Airlines' domestic route service. We use exact enumeration formulae to identify statistically over- and under-represented subgraphs, known as motifs and anti-motifs. We discover substantial topology transitions in Southwest's network and provide evidence for time-varying power-law scaling between subgraph counts and the number of edges in the network. We also suggest a node…
We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an $m$-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when $m$ scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the di…
McGill University（麦吉尔大学）；Montreal Institute for Learning Algorithms (MILA)（蒙特利尔学习算法研究所）；Institut Pasteur（巴斯德研究所）；Mines ParisTech（巴黎高等矿业学院）；Paris-Sciences-et-Lettres Research University（巴黎文理研究大学）
RNA 3D motifs are recurrent substructures, modelled as networks of base pair interactions, which are crucial for understanding structure-function relationships. The task of automatically identifying such motifs is computationally hard, and remains a key challenge in the field of RNA structural biology and network analysis. State of the art methods solve special cases of the motif problem by constraining the structural variability in occurrences of a motif, and narrowing the substructure search space. Here, we relax these constraints by posing the motif finding problem as a graph representation…
University of Oxford（牛津大学）；Princeton University（普林斯顿大学）；The Alan Turing Institute（阿兰·图灵研究所）；University of Glasgow（格拉斯哥大学）
Clustering is an essential technique for network analysis, with applications in a diverse range of fields. Although spectral clustering is a popular and effective method, it fails to consider higher-order structure and can perform poorly on directed networks. One approach is to capture and cluster higher-order structures using motif adjacency matrices. However, current formulations fail to take edge weights into account, and thus are somewhat limited when weight is a key component of the network under study. We address these shortcomings by exploring motif-based weighted spectral clustering me…
Historically studies of behaviour on networks have focused on the behaviour of individuals (node-based) or on the aggregate behaviour of the entire network. We propose a new method to decompose a temporal network into macroscale components and to analyse the behaviour of these components, or collectives of nodes, across time. This method utilises all available information in the temporal network (i.e. no temporal aggregation), combining both topological and temporal structure using temporal motifs and inter-event times. This allows us create an embedding of a temporal network in order to descr…
Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of individual nodes and edges. Thus, they fail to capture the higher-order characteristics at the level of small dense subgraph patterns, e.g., motifs. Recently, some higher-order methods have been developed but they typically focus on the motif-based hypergraph which is assumed to be a connected graph. However, such assumption cannot be ensured in some real-worl…
The availability of big data recorded from massively multiplayer online role-playing games (MMORPGs) allows us to gain a deeper understanding of the potential connection between individuals' network positions and their economic outputs. We use a statistical filtering method to construct dependence networks from weighted friendship networks of individuals. We investigate the 30 distinct motif positions in the 13 directed triadic motifs which represent microscopic dependences among individuals. Based on the structural similarity of motif positions, we further classify individuals into different …
A large number of real-world graphs or networks are inherently heterogeneous, involving a diversity of node types and relation types. Heterogeneous graph embedding is to embed rich structural and semantic information of a heterogeneous graph into low-dimensional node representations. Existing models usually define multiple metapaths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models either omit node content features, discard intermediate nodes along the metapath, or only consider one metapath. To address these three limitations, we p…
Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and online social networks (OSNs). Nowadays the massive size of some critical networks -- often stored in already overloaded relational databases -- effectively limits the rate at which nodes and edges can be explored, making it a challenge to accurately discover subgraph statistics. In this work, we propose sampling methods to accurately estimate subgraph statistics from as few queried nodes as possible. We present samplin…
Algorithms for mining very large graphs, such as those representing online social networks, to discover the relative frequency of small subgraphs within them are of high interest to sociologists, computer scientists and marketeers alike. However, the computation of these network motif statistics via naive enumeration is infeasible for either its prohibitive computational costs or access restrictions on the full graph data. Methods to estimate the motif statistics based on random walks by sampling only a small fraction of the subgraphs in the large graph address both of these challenges. In thi…
In friendship networks, individuals have different numbers of friends, and the closeness or intimacy between an individual and her friends is heterogeneous. Using a statistical filtering method to identify relationships about who depends on whom, we construct dependence networks (which are directed) from weighted friendship networks of avatars in more than two hundred virtual societies of a massively multiplayer online role-playing game (MMORPG). We investigate the evolution of triadic motifs in dependence networks. Several metrics show that the virtual societies evolved through a transient st…
