Social networks are now ubiquitous and most of them contain interactions involving multiple actors (groups) like author collaborations, teams or emails in an organizations, etc. Hypergraphs are natural structures to effectively capture multi-actor interactions which conventional dyadic graphs fail to capture. In this work the problem of predicting collaborations is addressed while modeling the collaboration network as a hypergraph network. The problem of predicting future multi-actor collaboration is mapped to hyperedge prediction problem. Given that the higher order edge prediction is an inherently hard problem, in this work we restrict to the task of predicting edges (collaborations) that have already been observed in past. In this work, we propose a novel use of hyperincidence temporal tensors to capture time varying hypergraphs and provides a tensor decomposition based prediction algorithm. We quantitatively compare the performance of the hypergraphs based approach with the conventional dyadic graph based approach. Our hypothesis that hypergraphs preserve the information that simple graphs destroy is corroborated by experiments using author collaboration network from the DBLP dataset. Our results demonstrate the strength of hypergraph based approach to predict higher order collaborations (size>4) which is very difficult using dyadic graph based approach. Moreover, while predicting collaborations of size>2 hypergraphs in most cases provide better results with an average increase of approx. 45 in F-Score for different sizes = 3,4,5,6,7 .
Hypergraphs can easily capture the higher-order relationships while incorporating both group and node level attributes. Moreover, research has shown that several social, biological, ecological and technological systems can be better modeled using hypergraphs than using dyadic proxies @cite_21 . There is an abundant literature of hypergraph theory in past @cite_15 and many work in the spectral theory of hypergraphs recently @cite_18 @cite_14 . The past decade has also seen an increasing interest for hypergraphs in machine learning community @cite_24 @cite_13 . Hypergraphs have been used to model complex networks in different fields including biology @cite_23 , databases @cite_8 and data mining @cite_1 . In the domain of social sciences, Kapoor et a.l @cite_20 have proposed with centrality metrics for weighted hypergraphs. @cite_19 propose hypergraphs based metrics to evaluate various hypothesis, both semantic and structural, regarding team formation.
@cite_18 @cite_14 @cite_8 @cite_21 @cite_1 @cite_24 @cite_19 @cite_23 @cite_15 @cite_13 @cite_20
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Many real-world social interactions involve multiple people, for e.g., authors collaborating on a paper, email exchanges made in a company and task-oriented teams in workforce. Simple graph representation of these activities destroys the group structure present in them. Hypergraphs have recently emerged as a better tool for modeling group interactions. However, methods in social hypernetwork analysis haven't kept pace. In this work, we extend the concept of node degree centrality to hypergraphs. We validate our proposed measures using alternate measures of influence available to us using two datasets namely, the DBLP dataset of scientific collaborations and the group network in a popular Chinese multi-player online game called CR3. We discuss several schemes for assigning weights to hyperedges and compare them empirically. Finally, we define separate weak and strong tie node degree centralities which improves performance of our models. Weak tie degree centrality is found to be a better predictor of influence in hypergraphs than strong tie degree centrality. In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hypergraph, which is more flexible on data modeling, especially when dealing with complex data. In this method, a hyperedge convolution operation is designed to handle the data correlation during representation learning. In this way, traditional hypergraph learning procedure can be conducted using hyperedge convolution operations efficiently. HGNN is able to learn the hidden layer representation considering the high-order data structure, which is a general framework considering the complex data correlations. We have conducted experiments on citation network classification and visual object recognition tasks and compared HGNN with graph convolutional networks and other traditional methods. Experimental results demonstrate that the proposed HGNN method outperforms recent state-of-theart methods. We can also reveal from the results that the proposed HGNN is superior when dealing with multi-modal data compared with existing methods. Driven by the importance of relational aspects of data to decision-making, graph algorithms have been developed, based on simplified pairwise relationships, to solve a variety of problems. However, evidence has shown that hypergraphs—generalizations of graphs with (hyper)edges that connect any number of vertices—can better model complex, non-pairwise relationships in data and lead to better informed decisions. In this work, we compare graph and hypergraph models in the context of spectral clustering. For these problems, we demonstrate that hypergraphs are computationally more efficient and can better model complex, non-pairwise relationships for many datasets. Many real-world domains can be represented as large node-link graphs: backbone Internet routers connect with 70,000 other hosts, mid-sized Web servers handle between 20,000 and 200,000 hyperlinked documents, and dictionaries contain millions of words defined in terms of each other. Computational manipulation of such large graphs is common, but previous tools for graph visualization have been limited to datasets of a few thousand nodes. Visual depictions of graphs and networks are external representations that exploit human visual processing to reduce the cognitive load of many tasks that require understanding of global or local structure. We assert that the two key advantages of computer-based systems for information visualization over traditional paper-based visual exposition are interactivity and scalability. We also argue that designing visualization software by taking the characteristics of a target user's task domain into account leads to systems that are more effective and scale to larger datasets than previous work. This thesis contains a detailed analysis of three specialized systems for the interactive exploration of large graphs, relating the intended tasks to the spatial layout and visual encoding choices. We present two novel algorithms for specialized layout and drawing that use quite different visual metaphors. The H3 system for visualizing the hyperlink structures of web sites scales to datasets of over 100,000 nodes by using a carefully chosen spanning tree as the layout backbone, 3D hyperbolic geometry for a Focus+Context view, and provides a fluid interactive experience through guaranteed frame rate drawing. The Constellation system features a highly specialized 2D layout intended to spatially encode domain-specific information for computational linguists checking the plausibility of a large semantic network created from dictionaries. The Planet Multicast system for displaying the tunnel topology of the Internet's multicast backbone provides a literal 3D geographic layout of arcs on a globe to help MBone maintainers find misconfigured long-distance tunnels. Each of these three systems provides a very different view of the graph structure, and we evaluate their efficacy for the intended task. We generalize these findings in our analysis of the importance of interactivity and specialization for graph visualization systems that are effective and scalable. In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the existing techniques to seek graph modes by shifting vertices based on pair-wise edges (i.e, an edge with 2 ends), our paradigm is based on shifting high-order edges (hyperedges) to deliver graph modes. Specifically, we convert the problem of seeking graph modes as the problem of seeking maximizers of a novel objective function with the aim to generate good graph modes based on sifting edges in hypergraphs. As a result, the generated graph modes based on dense subhypergraphs may more accurately capture the object semantics besides the self-cohesiveness requirement. We also formally prove that our technique is always convergent. Extensive empirical studies on synthetic and real world data sets are conducted on clustering and graph matching. They demonstrate that our techniques significantly outperform the existing techniques. A hypergraph is a generalization of the traditional graph in which the edges are arbitrary non-empty subsets of the vertex set. It has been applied successfully to capture high-order relations in various domains. In this paper, we propose a hypergraph spectral learning formulation for multi-label classification, where a hypergraph is constructed to exploit the correlation information among different labels. We show that the proposed formulation leads to an eigenvalue problem, which may be computationally expensive especially for large-scale problems. To reduce the computational cost, we propose an approximate formulation, which is shown to be equivalent to a least squares problem under a mild condition. Based on the approximate formulation, efficient algorithms for solving least squares problems can be applied to scale the formulation to very large data sets. In addition, existing regularization techniques for least squares can be incorporated into the model for improved generalization performance. We have conducted experiments using large-scale benchmark data sets, and experimental results show that the proposed hypergraph spectral learning formulation is effective in capturing the high-order relations in multi-label problems. Results also indicate that the approximate formulation is much more efficient than the original one, while keeping competitive classification performance. Relational phrases (e.g., “got married to”) and their hypernyms (e.g., “is a relative of”) are central for many tasks including question answering, open information extraction, paraphrasing, and entailment detection. This has motivated the development of several linguistic resources (e.g. DIRT, PATTY, and WiseNet) which systematically collect and organize relational phrases. These resources have demonstrable practical benefits, but are each limited due to noise, sparsity, or size. We present a new general-purpose method, RELLY, for constructing a large hypernymy graph of relational phrases with high-quality subsumptions using collective probabilistic programming techniques. Our graph induction approach integrates small highprecision knowledge bases together with large automatically curated resources, and reasons collectively to combine these resources into a consistent graph. Using RELLY, we construct a high-coverage, high-precision hypernymy graph consisting of 20K relational phrases and 35K hypernymy links. Our evaluation indicates a hypernymy link precision of 78 , and demonstrates the value of this resource for a document-relevance ranking task. Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size t to belong to the hypergraph depends of a parameter ω t of the model. It is a natural generalization of the models of graphs used by Flajolet, Knuth and Pittel 11] and Janson, Knuth, Łuczak and Pittel 16]. The present paper follows the same general approach based on analytic combinatorics. We show that many analytic tools developed for the analysis of graphs can be extended surprisingly well to non-uniform hypergraphs. More specifically, we analyze their typical structure before and near the birth of the complex components, that are the connected components with more than one cycle. We derive the asymptotic number of sparse connected hypergraphs as their complexity, defined as the excess, increases. Although less natural than the number of edges, this parameter allows a precise description of the structure of hypergraphs. Finally, we compute some statistics of the model to link number of edges and excess. In this work, we show the deficiencies of the graph model for decomposing sparse matrices for parallel matrix-vector multiplication. Then, we propose two hypergraph models which avoid all deficiencies of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem widely encountered in circuit partitioning in VLSI. We have implemented fast Kernighan-Lin based graph and hypergraph partitioning heuristics and used the successful multilevel graph partitioning tool (Metis) for the experimental evaluation of the validity of the proposed hypergraph models. We have also developed a multilevel hypergraph partitioning heuristic for experimenting the performance of the multilevel approach on hypergraph partitioning. Experimental results on sparse matrices, selected from Harwell-Boeing collection and NETLIB suite, confirm both the validity of our proposed hypergraph models and appropriateness of the multilevel approach to hypergraph partitioning. Recent advances in network science allows the modeling and analysis of complex inter-related entities. These entities often interact with each other in a number of different ways. Simple graphs fail to capture these multiple types of relationships requiring more sophisticated mathematical structures. One such structure is multigraph, where entities (or nodes) can be linked to each other through multiple edges. In this paper we describe a new method to manage multiple types of relationships existing in multigraphs. Our approach is based on the concept of pair of nodes (edges) and, in particular, we study how nodes on different layers interact which each other considering the edges they share. We propose a two level strategy that summarizes global local multigraph features. The global view helps us to gain knowledge related to the characteristics of layers and how they interact while the local view provides an analysis of individual layers highlighting edge properties such as cluster structure. Our proposal is complementary to standard node-link diagram and it can be coupled with such techniques in order to intelligently explore multigraphs. The proposed visualization is tested on a real world case study and the outcomes point out the ability of our proposal to discover patterns present in the data. Given multimillion-node graphs such as "who-follows-whom", "patent-cites-patent", "user-likes-page" and "actor director-makes-movie" networks, how can we find unexpected behaviors? When companies operate on the graphs with monetary incentives to sell Twitter "Followers" and Facebook page "Likes", the graphs show strange connectivity patterns. In this paper, we study a complete graph from a large Twitter-style social network, spanning up to 3.33 billion edges. We report strange deviations from typical patterns like smooth degree distributions. We find that such deviations are often due to "lockstep behavior" that large groups of followers connect to the same groups of followees. Our first contribution is that we study strange patterns on the adjacency matrix and in the spectral subspaces with respect to several flavors of lockstep. We discover that (a) the lockstep behaviors on the graph shape dense "block" in its adjacency matrix and creates "rays" in spectral subspaces, and (b) partially overlapping of the behaviors shape "staircase" in its adjacency matrix and creates "pearls" in spectral subspaces. The second contribution is that we provide a fast algorithm, using the discovery as a guide for practitioners, to detect users who offer the lockstep behaviors in undirected directed bipartite graphs. We carry out extensive experiments on both synthetic and real datasets, as well as public datasets from IMDb and US Patent. The results demonstrate the scalability and effectiveness of our proposed algorithm.