One-mode Projections Research Articles

Network analysis of driver genes in human cancers.

Cancer is a heterogeneous disease that results from genetic alteration of cell cycle and proliferation controls. Identifying mutations that drive cancer, understanding cancer type specificities, and delineating how driver mutations interact with each other to establish disease is vital for identifying therapeutic vulnerabilities. Such cancer specific patterns and gene co-occurrences can be identified by studying tumor genome sequences, and networks have proven effective in uncovering relationships between sequences. We present two network-based approaches to identify driver gene patterns among tumor samples. The first approach relies on analysis using the Directed Weighted All Nearest Neighbors (DiWANN) model, which is a variant of sequence similarity network, and the second approach uses bipartite network analysis. A data reduction framework was implemented to extract the minimal relevant information for the sequence similarity network analysis, where a transformed reference sequence is generated for constructing the driver gene network. This data reduction process combined with the efficiency of the DiWANN network model, greatly lowered the computational cost (in terms of execution time and memory usage) of generating the networks enabling us to work at a much larger scale than previously possible. The DiWANN network helped us identify cancer types in which samples were more closely connected to each other suggesting they are less heterogeneous and potentially susceptible to a common drug. The bipartite network analysis provided insight into gene associations and co-occurrences. We identified genes that were broadly mutated in multiple cancer types and mutations exclusive to only a few. Additionally, weighted one-mode gene projections of the bipartite networks revealed a pattern of occurrence of driver genes in different cancers. Our study demonstrates that network-based approaches can be an effective tool in cancer genomics. The analysis identifies co-occurring and exclusive driver genes and mutations for specific cancer types, providing a better understanding of the driver genes that lead to tumor initiation and evolution.

Two-mode relational similarities

In a previous paper, Kovacs (2010) proposed a generalized relational similarity measure based on iterated correlations of entities in a network calibrated by their relational similarity to other entities. Here I show that, in the case of two-mode network data, Kovacs’s approach can be simplified and generalized similarities calculated non-iteratively. The basic idea is to rely on initial similarities calculated from transforming the two-mode data into one-mode projections using the familiar duality approach due to Breiger (1974). I refer to this as two-mode relational similarities and show, using the Southern Women’s data and data from Senate voting in the 112th U.S. Congress, that it yields results substantively indistinguishable from Kovacs’s iterative strategy.

“Offending with the accomplices of my accomplices”: Evidence and implications regarding triadic closure in co-offending networks

We measured triadic closure in co-offending networks – i.e., the tendency of two individuals to co-offend if they share an accomplice – using a method that addresses the risk of overestimating clustering coefficients when using one-mode projections. We also assess the statistical significance of clustering coefficients using null models. The data relates to adult offenders (N = 274,689) connected to criminal investigations (N = 286,591) in Colombia. The observed coefficients range between 0.05 and 0.53 and are statistically significant, indicating that accomplices become sources of information about potential associates. They support the idea of preventing crime by targeting offenders’ trustworthiness and disrupting information flows.

The role of bipartite structure in R&D collaboration networks

AbstractA great number of real-world networks are, in fact, one-mode projections of bipartite networks comprised of two different types of nodes. In the case of interactions between institutions engaging in collaboration for technological innovation, the underlying network is bipartite with institutions (agents) linked to the patents they have filed (artefacts), while the projection is the co-patenting network. Since projected network properties are highly affected by the underlying bipartite structure a lack of understanding of the bipartite network has consequences for the information that might be drawn from the one-mode co-patenting network. Here, we create an empirical bipartite network using data from 2.7 million patents recorded by the European Patent Office. We project this network onto the agents (institutions) and look at properties of both the bipartite and projected networks that may play a role in knowledge sharing and collaboration. We compare these empirical properties to those of synthetic bipartite networks and their projections. We show that understanding the bipartite network topology is critical for understanding the potential flow of technological knowledge. Properties of the bipartite structure, such as degree distributions and small cycles, affect the topology of the one-mode projected network—specifically degree and clustering distributions, and degree assortativity. We propose new network-based metrics as a way to quantify how collaborative agents are in the collaboration network. We find that several large corporations are the most collaborative agents in the network; however, such organizations tend to have a low diversity of collaborators. In contrast, the most prolific institutions tend to collaborate relatively little but with a diverse set of collaborators. This indicates that they concentrate the knowledge of their core technical research while seeking specific complementary knowledge via collaboration with smaller institutions.

Using network science to unveil badminton performance patterns

Abstract Bipartite networks are related to non-linear and ecological approaches where, at least, two different kinds of entities are considered. In sports, we can consider players as entities that base their decisions (actions and reactions) on opponents and their own actions. Incorporation of bipartite networks into modelling of racket sport performances may bridge the gap between the performance analysis sub-discipline and coaches for greater preparation of training sessions and competitions for enhanced success. Thus, the main aim of this study was to create badminton stroke networks (BSN), from the match activities of a player and their opponents, to describe and quantify the performance of elite Olympic badminton players. The use of a Network Science approach required the development of a series of methodologies that accounted for strokes played by all medallists within an Olympic tournament and included: (i) the construction of BSN; (ii) the one-mode projections of bipartite networks (self- and opponent- networks); (iii) the centrality of one-mode projections; and (iv) the identifiability of badminton players. The BSN identified different playing patterns for medallists with the Silver medallist categorised with the less predictable and defined style of play, the Bronze medallist exhibiting the most defined style; and the Gold medallist exhibiting the greatest predictability, but only when losing points (self-networks). The use of Network Science enabled the identification of distinctive styles of play (self- and opponent–related), based on stroke performance, during successful and unsuccessful points within an Olympic tournament. Specifically, the identifiability of each player's network and its associations with point outcome, provided a better understanding of stroke performances and individual features of world-class badminton players. The use of non-linear approaches (such as bipartite networks) to measure and visualize player's performances, accounting for the specific nature of badminton and opponents, may support coaches and players with the contextualized demands of playing patterns and their performances (i.e., winning and losing points) for future success.

MANET 3.0: Hierarchy and modularity in evolving metabolic networks.

Enzyme recruitment is a fundamental evolutionary driver of modern metabolism. We see evidence of recruitment at work in the metabolic Molecular Ancestry Networks (MANET) database, an online resource that integrates data from KEGG, SCOP and structural phylogenomic reconstruction. The database, which was introduced in 2006, traces the deep history of the structural domains of enzymes in metabolic pathways. Here we release version 3.0 of MANET, which updates data from KEGG and SCOP, links enzyme and PDB information with PDBsum, and traces evolutionary information of domains defined at fold family level of SCOP classification in metabolic subnetwork diagrams. Compared to SCOP folds used in the previous versions, fold families are cohesive units of functional similarity that are highly conserved at sequence level and offer a 10-fold increase of data entries. We surveyed enzymatic, functional and catalytic site distributions among superkingdoms showing that ancient enzymatic innovations followed a biphasic temporal pattern of diversification typical of module innovation. We grouped enzymatic activities of MANET into a hierarchical system of subnetworks and mesonetworks matching KEGG classification. The evolutionary growth of these modules of metabolic activity was studied using bipartite networks and their one-mode projections at enzyme, subnetwork and mesonetwork levels of organization. Evolving metabolic networks revealed patterns of enzyme sharing that transcended mesonetwork boundaries and supported the patchwork model of metabolic evolution. We also explored the scale-freeness, randomness and small-world properties of evolving networks as possible organizing principles of network growth and diversification. The network structure shows an increase in hierarchical modularity and scale-free behavior as metabolic networks unfold in evolutionary time. Remarkably, this evolutionary constraint on structure was stronger at lower levels of metabolic organization. Evolving metabolic structure reveals a ‘principle of granularity’, an evolutionary increase of the cohesiveness of lower-level parts of a hierarchical system. MANET is available at http://manet.illinois.edu.

Structural cohesion and embeddedness in two-mode networks

ABSTRACT The detection of structural cohesion is a key utility of social network analysis, but little work has been done to refine the detection of structural cohesion in two-mode networks. Most work on cohesion in two-mode networks either: (1) attempts to detect cohesion in such networks using one-mode projections (which can be problematic for reasons we discuss); or (2) focuses on restrictive substructures like bi-cliques to identify cohesive subgroups. We propose a new strategy for two-mode networks that follows the general reasoning of approaches to detecting structural cohesion in one-mode networks. Our approach identifies the number of actors from one node set that may be removed before disconnecting actors in the opposite set. We also develop a definition of embeddedness that draws on Moody and White’s hierarchical nesting approach.

Degree distributions of bipartite networks and their projections.

Bipartite (two-mode) networks are important in the analysis of social and economic systems as they explicitly show conceptual links between different types of entities. However, applications of such networks often work with a projected (one-mode) version of the original bipartite network. The topology of the projected network, and the dynamics that take place on it, are highly dependent on the degree distributions of the two different node types from the original bipartite structure. To date, the interaction between the degree distributions of bipartite networks and their one-mode projections is well understood for only a few cases, or for networks that satisfy a restrictive set of assumptions. Here we show a broader analysis in order to fill the gap left by previous studies. We use the formalism of generating functions to prove that the degree distributions of both node types in the original bipartite network affect the degree distribution in the projected version. To support our analysis, we simulate several types of synthetic bipartite networks using a configuration model where node degrees are assigned from specific probability distributions, ranging from peaked to heavy-tailed distributions. Our findings show that when projecting a bipartite network onto a particular set of nodes, the degree distribution for the resulting one-mode network follows the distribution of the nodes being projected on to, but only so long as the degree distribution for the opposite set of nodes does not have a heavier tail. Furthermore, we show that bipartite degree distributions are not the only feature driving topology formation of projected networks, in contrast to what is commonly described in the literature.

Structural holes and bridging in two-mode networks

Social networks are often structured in such a way that there are gaps, or “structural holes,” between regions. Some actors are in the position to bridge or span these gaps, giving rise to individual advantages relating to brokerage, gatekeeping, access to non-redundant contacts, and control over network flows. The most widely used measures of a given actor’s bridging potential gauge the extent to which that actor is directly connected to others who are otherwise not well connected to each other. Unfortunately, the measures that have been developed to identify structural holes cannot be adapted directly to two-mode networks, like individual-to-organization networks. In two-mode networks, direct contacts cannot be directly connected to each other by definition, making the calculation of redundancy, effective size, and constraint impossible with conventional one-mode methods. We therefore describe a new framework for the measurement of bridging in two-mode networks that hinges on the mathematical concept of the intersection of sets. An actor in a given node class (“ego”) has bridging potential to the extent that s/he is connected to actors in the opposite node class that have unique profiles of connections to actors in ego’s own node class. We review the relevant literature pertaining to structural holes in two-mode networks, and we compare our primary bridging measure (effective size) to measures of bridging that result when using one-mode projections of two-mode data. We demonstrate the results of applying our approach to empirical data on the organizational affiliations of elites in a large U.S. city.

Understanding User Behavior in Sina Weibo Online Social Network: A Community Approach

Sina Weibo, a Twitter-like microblogging Website in China, has become the main source of different kinds of information, such as breaking news, social events, and products. There is great value to exploiting the actual interests and behaviors of users, which creates opportunity for better understanding of the information dissemination mechanisms on social network sites. In this paper, we focus our attention to characterizing user behaviors in tweeting, retweeting, and commenting on Sina Weibo. In particular, we built a Shenzhen Weibo community graph to analyze user behaviors, clustering the coefficients of the community graph and exploring the impact of user popularity on social network sites. Bipartite graphs and one-mode projections are used to analyze the similarity of retweeting and commenting activities, which reveal the weak correlations between these two behaviors. In addition, to characterize the user retweeting behaviors deeply, we also study the tweeting and retweeting behaviors in terms of the gender of users. We observe that females are more likely to retweet than males. This discovery is useful for improving the efficiency of message transmission. What is more, we introduce an information-theoretical measure based on the concept of entropy to analyze the temporal tweeting behaviors of users. Finally, we apply a clustering algorithm to divide users into different groups based on their tweeting behaviors, which can improve the design of plenty of applications, such as recommendation systems.

Latent geometry of bipartite networks.

Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

Modeling one-mode projection of bipartite networks by tagging vertex information

Abstract Traditional one-mode projection models are less informative than their original bipartite networks. Hence, using such models cannot control the projection’s structure freely. We proposed a new method for modeling the one-mode projection of bipartite networks, which thoroughly breaks through the limitations of the available one-mode projecting methods by tagging the vertex information of bipartite networks in their one-mode projections. We designed a one-mode collaboration network model by using the method presented in this paper. The simulation results show that our model matches three real networks very well and outperforms the available collaboration network models significantly, which reflects the idea that our method is ideal for modeling one-mode projection models of bipartite graphs and that our one-mode collaboration network model captures the crucial mechanisms of the three real systems. Our study reveals that size growth, individual aging, random collaboration, preferential collaboration, transitivity collaboration and multi-round collaboration are the crucial mechanisms of collaboration networks, and the lack of some of the crucial mechanisms is the main reason that the other available models do not perform as well as ours.

Fast extraction of the backbone of projected bipartite networks to aid community detection

This paper introduces a computationally inexpensive method for 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 information in the one-mode projection to the most relevant. We demonstrate that the backbone of a one-mode projection aids in the detection of communities.

Efficiently inferring community structure in bipartite networks.

Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts, existing approaches to bipartite community detection have drawbacks, including implicit parameter choices, loss of information through one-mode projections, and lack of interpretability. Here we solve the community detection problem for bipartite networks by formulating a bipartite stochastic block model, which explicitly includes vertex type information and may be trivially extended to k-partite networks. This bipartite stochastic block model yields a projection-free and statistically principled method for community detection that makes clear assumptions and parameter choices and yields interpretable results. We demonstrate this model's ability to efficiently and accurately find community structure in synthetic bipartite networks with known structure and in real-world bipartite networks with unknown structure, and we characterize its performance in practical contexts.

Behavior Analysis of Internet Traffic via Bipartite Graphs and One-Mode Projections

As Internet traffic continues to grow in size and complexity, it has become an increasingly challenging task to understand behavior patterns of end-hosts and network applications. This paper presents a novel approach based on behavioral graph analysis to study the behavior similarity of Internet end-hosts. Specifically, we use bipartite graphs to model host communications from network traffic and build one-mode projections of bipartite graphs for discovering social-behavior similarity of end-hosts. By applying simple and efficient clustering algorithms on the similarity matrices and clustering coefficient of one-mode projection graphs, we perform network-aware clustering of end-hosts in the same network prefixes into different end-host behavior clusters and discover inherent clustered groups of Internet applications. Our experiment results based on real datasets show that end-host and application behavior clusters exhibit distinct traffic characteristics that provide improved interpretations on Internet traffic. Finally, we demonstrate the practical benefits of exploring behavior similarity in profiling network behaviors, discovering emerging network applications, and detecting anomalous traffic patterns.

Small Worlds in Networks of Inventors and the Role of Academics: An Analysis of France

Using data on patent applications at the European Patent Office, we examine the structural properties of networks of inventors in France in different technologies. We find that the higher the presence of inventors from universities and public research organizations (PROs), the more likely the networks are to exhibit small world properties. University and PRO inventors contribute to reduce average path length insofar they are more mobile (across applicants) than other inventors, thus linking up otherwise disconnected cliques. We achieve these results by implementing an original methodology for detecting small world properties in one-mode projections of two-mode graphs.

Identifying statistically significant edges in one-mode projections

One-mode projections of two-mode data are typically valued, and therefore, require dichotomization before they can be analyzed using many network analytic methods. The traditional dichotomization approach, in which a universal threshold is applied to all edge weights, can yield a binary one-mode projection with undesirable artifacts and requires the arbitrary selection of a threshold value. This paper proposes a method and associated Stata command, ONEMODE, for identifying statistically significant edges in one-mode projections, which can be used to construct both binary and signed projections. The method is demonstrated using two-mode data on southern women’s social event participation and US Supreme Court justices’ majority decision participation, and is compared to two alternative approaches for normalizing edge weights in one-mode projections.

Degree distributions of evolving alphabetic bipartite networks and their projections

Many real-world systems are modeled as evolving bipartite networks and their one-mode projections. In particular, Discrete Combinatorial Systems (DCSs), which consist of a finite set of elementary units and different combinations of these units, can be modeled by a subclass of bipartite networks known as Alphabetic Bipartite Networks or α-BiNs, where the bottom partite-set contains a fixed number of nodes (the elementary units) and the top partite-set grows unboundedly with time through the addition of nodes (the combinations). The principal questions in the study of α-BiN evolution are to predict the degree distribution of the bottom set and that of the projection onto the bottom set (the bottom projection), from a knowledge of the bipartite growth dynamics. In this paper, we propose a realistic growth model for α-BiNs, where the degree distribution of the top set (i.e., the distribution of the number of elementary units in the composite entities in the DCS) can be any arbitrary distribution with finite first and second moments. Utilizing an exact correspondence between the preferential growth of α-BiNs and the Polya Urn scheme, we analytically solve the model to compute exact degree distributions of the bottom (fixed) set and the bottom projection. To the best of our knowledge, this is the first work which proposes and solves such a generalized growth model for α-BiNs. We also derive that the degree distributions of both the bottom set and the bottom projection, suitably normalized with time, converge to distributions that are invariant over time. We also verify that this improved model can accurately explain the degree distributions of several real-world DCSs and their projections.

A systematic approach to the one-mode projection of bipartite graphs

Bipartite graphs are common in many complex systems as they describe a relationship between two different kinds of actors, e.g., genes and proteins, metabolites and enzymes, authors and articles, or products and consumers. A common approach to analyze them is to build a graph between the nodes on one side depending on their relationships with nodes on the other side; this so-called one-mode projection is a crucial step for all further analysis but a systematic approach to it was lacking so far. Here, we present a systematic approach that evaluates the significance of the co-occurrence for each pair of nodes v, w, i.e., the number of common neighbors of v and w. It turns out that this can be seen as a special case of evaluating the interestingness of an association rule in data mining. Based on this connection we show that classic interestingness measures in data mining cannot be applied to evaluate most real-world product-consumer relationship data. We thus introduce generalized interestingness measures for both, one-mode projections of bipartite graphs and data mining and show their robustness and stability by example. We also provide theoretical results that show that the old method cannot even be used as an approximative method. In a last step we show that the new interestingness measures show stable and significant results that result in attractive one-mode projections of bipartite graphs.

Modeling discrete combinatorial systems as alphabetic bipartite networks: Theory and applications

Genes and human languages are discrete combinatorial systems (DCSs), in which the basic building blocks are finite sets of elementary units: nucleotides or codons in a DNA sequence, and letters or words in a language. Different combinations of these finite units give rise to potentially infinite numbers of genes or sentences. This type of DCSs can be represented as an alphabetic bipartite network (ABN) where there are two kinds of nodes, one type represents the elementary units while the other type represents their combinations. Here, we extend and generalize recent analytical findings for ABNs derived in [Peruani, Europhys. Lett. 79, 28001 (2007)] and empirically investigate two real world systems in terms of ABNs, the codon gene and the phoneme-language network. The one-mode projections onto the elementary basic units are also studied theoretically as well as in real world ABNs. We propose the use of ABNs as a means for inferring the mechanisms underlying the growth of real world DCSs.