We propose a method for extracting hierarchical backbones from a bipartite network. Our method leverages the observation that a hierarchical relationship between two nodes in a bipartite network is often manifested as an asymmetry in the conditional probability of observing the connections to them from the other node set. Our method estimates both the importance and direction of the hierarchical relationship between a pair of nodes, thereby providing a flexible way to identify the essential part of the networks. Using semi-synthetic benchmarks, we show that our method outperforms existing methods at identifying planted hierarchy while offering more flexibility. Application of our method to empirical datasets---a bipartite network of skills and individuals as well as the network between gene products and Gene Ontology (GO) terms---demonstrates the possibility of automatically extracting or augmenting ontology from data.
Bipartite projections are used in a wide range of network contexts including politics (bill co-sponsorship), genetics (gene co-expression), economics (executive board co-membership), and innovation (patent co-authorship). However, because bipartite projections are always weighted graphs, which are inherently challenging to analyze and visualize, it is often useful to examine the 'backbone', an unweighted subgraph containing only the most significant edges. In this paper, we introduce the R package backbone for extracting the backbone of weighted bipartite projections, and use bill sponsorship …
This paper introduces a computationally inexpensive method of extracting the backbone of one-mode networks projected from bipartite networks. We show that the edge weights in the one-mode projections are distributed according to a Poisson binomial distribution and that finding the expected weight distribution of a one-mode network projected from a random bipartite network only requires knowledge of the bipartite degree distributions. Being able to extract the backbone of a projection is highly beneficial in filtering out redundant information in large complex networks and narrowing down the in…
The central problem of concern to Serrano, Boguna and Vespignani ("Extracting the multiscale backbone of complex weighted networks", Proc Natl Acad Sci 106:6483-6488 [2009]) can be effectively and elegantly addressed using a well-established two-stage algorithm that has been applied to internal migration flows for numerous nations and several other forms of "transaction flow data".
Projections of bipartite or two-mode networks capture co-occurrences, and are used in diverse fields (e.g., ecology, economics, bibliometrics, politics) to represent unipartite networks. A key challenge in analyzing such networks is determining whether an observed number of co-occurrences between two nodes is significant, and therefore whether an edge exists between them. One approach, the fixed degree sequence model (FDSM), evaluates the significance of an edge's weight by comparison to a null model in which the degree sequences of the original bipartite network are fixed. Although the FDSM i…
Network science provides effective tools to model and analyze complex systems. However, the increasing size of real-world networks becomes a major hurdle in order to understand their structure and topological features. Therefore, mapping the original network into a smaller one while preserving its information is an important issue. Extracting the so-called backbone of a network is a very challenging problem that is generally handled either by coarse-graining or filter-based methods. Coarse-graining methods reduce the network size by grouping similar nodes, while filter-based methods prune the …
Networks provide useful tools for analyzing diverse complex systems from natural, social, and technological domains. Growing size and variety of data such as more nodes and links and associated weights, directions, and signs can provide accessory information. Link and weight abundance, on the other hand, results in denser networks with noisy, insignificant, or otherwise redundant data. Moreover, typical network analysis and visualization techniques presuppose sparsity and are not appropriate or scalable for dense and weighted networks. As a remedy, network backbone extraction methods aim to re…
Information overload is a serious problem in modern society and many solutions such as recommender system have been proposed to filter out irrelevant information. In the literature, researchers mainly dedicated to improve the recommendation performance (accuracy and diversity) of the algorithms while overlooked the influence of topology of the online user-object bipartite networks. In this paper, we find that some information provided by the bipartite networks is not only redundant but also misleading. With such "less can be more" feature, we design some algorithms to improve the recommendatio…
Networks are useful for representing phenomena in a broad range of domains. Although their ability to represent complexity can be a virtue, it is sometimes useful to focus on a simplified network that contains only the most important edges: the backbone. This paper introduces and demonstrates the `backbone' package for R, which implements methods for extracting the backbone from weighted networks, weighted bipartite projections, and unweighted networks. For each type of network, fully replicable code is presented first for small toy examples, then for complete empirical examples using transpor…
According to the Eurobarometer report about EU media use of May 2018, the number of European citizens who consult on-line social networks for accessing information is considerably increasing. In this work we analyze approximately $10^6$ tweets exchanged during the last Italian elections. By using an entropy-based null model discounting the activity of the users, we first identify potential political alliances within the group of verified accounts: if two verified users are retweeted more than expected by the non-verified ones, they are likely to be related. Then, we derive the users' affiliati…
State Key Lab of Software Development Environment, Beihang University（北京航空航天大学软件开发环境国家重点实验室）；School of Statistics, Capital University of Economics and Business（首都经济贸易大学统计学院）
Given the development and abundance of social media, studying the stance of social media users is a challenging and pressing issue. Social media users express their stance by posting tweets and retweeting. Therefore, the homogeneous relationship between users and the heterogeneous relationship between users and tweets are relevant for the stance detection task. Recently, graph neural networks (GNNs) have developed rapidly and have been applied to social media research. In this paper, we crawl a large-scale dataset of the 2020 US presidential election and automatically label all users by manual…
The complementarity and substitutability between products are essential concepts in retail and marketing. Qualitatively, two products are said to be substitutable if a customer can replace one product by the other, while they are complementary if they tend to be bought together. In this article, we take a network perspective to help automatically identify complements and substitutes from sales transaction data. Starting from a bipartite product-purchase network representation, with both transaction nodes and product nodes, we develop appropriate null models to infer significant relations, eith…
Rumor Detection with Hierarchical Representation on Bipartite Adhoc Event Trees
University of Technology Sydney（悉尼科技大学）；Beijing Institute of Technology（北京理工大学）；Tongji University（同济大学）；DeepBlue Academy of Sciences（深兰科学院）；University of Sydney（悉尼大学）
A convex network can be defined as a network such that every connected induced subgraph includes all the shortest paths between its nodes. Fully convex network would therefore be a collection of cliques stitched together in a tree. In this paper, we study the largest high-convexity part of empirical networks obtained by removing the least number of edges, which we call a convex skeleton. A convex skeleton is a generalisation of a network spanning tree in which each edge can be replaced by a clique of arbitrary size. We present different approaches for extracting convex skeletons and apply them…
To control for multiscale effects in networks, one can transform the matrix of (in general) weighted, directed internodal flows to bistochastic (doubly-stochastic) form, using the iterative proportional fitting (Sinkhorn-Knopp) procedure, which alternatively scales row and column sums to all equal 1. The dominant entries in the bistochasticized table can then be employed for network reduction, using strong component hierarchical clustering. We illustrate various facets of this well-established, widely-applied two-stage algorithm with the 3, 107 x 3, 107 (asymmetric) 1995-2000 intercounty migra…
