Identifying Influential Nodes in Bipartite Networks Using the Clustering Coefficient

The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities

The role of bipartite structure in R&D collaboration networks

A number of real-world networks are, in fact, one-mode projections of bipartite networks comprised of two types of nodes. For institutions engaging in collaboration for technological innovation, the underlying network is bipartite with institutions (agents) linked to the patents they have filed (artifacts), while the projection is the co-patenting network. Projected network topology is highly affected by the underlying bipartite structure, hence 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. 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 in order to understand the processes that might operate in the network formation. A good understanding of the topology is critical for investigating the potential flow of technological knowledge. We show how degree distributions and small cycles affect the topology of the one-mode projected network - specifically degree and clustering distributions, and assortativity. We propose new network-based metrics to quantify how collaborative agents are in the co-patenting network. We find that several large corporations that are the most collaborative agents in the network, however such organisations 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 companies.Comment: 23 pages, 12 figures, 2 table

Predicting Item Popularity: Analysing Local Clustering Behaviour of Users

Predicting the popularity of items in rating networks is an interesting but challenging problem. This is especially so when an item has first appeared and has received very few ratings. In this paper, we propose a novel approach to predicting the future popularity of new items in rating networks, defining a new bipartite clustering coefficient to predict the popularity of movies and stories in the MovieLens and Digg networks respectively. We show that the clustering behaviour of the first user who rates a new item gives insight into the future popularity of that item. Our method predicts, with a success rate of over 65% for the MovieLens network and over 50% for the Digg network, the future popularity of an item. This is a major improvement on current results.Comment: 25 pages, 11 figure

Tunable and Growing Network Generation Model with Community Structures

Recent years have seen a growing interest in the modeling and simulation of social networks to understand several social phenomena. Two important classes of networks, small world and scale free networks have gained a lot of research interest. Another important characteristic of social networks is the presence of community structures. Many social processes such as information diffusion and disease epidemics depend on the presence of community structures making it an important property for network generation models to be incorporated. In this paper, we present a tunable and growing network generation model with small world and scale free properties as well as the presence of community structures. The major contribution of this model is that the communities thus created satisfy three important structural properties: connectivity within each community follows power-law, communities have high clustering coefficient and hierarchical community structures are present in the networks generated using the proposed model. Furthermore, the model is highly robust and capable of producing networks with a number of different topological characteristics varying clustering coefficient and inter-cluster edges. Our simulation results show that the model produces small world and scale free networks along with the presence of communities depicting real world societies and social networks.Comment: Social Computing and Its Applications, SCA 13, Karlsruhe : Germany (2013

Identifying significant behaviour in complex bipartite networks

The study of complex networks has received much attention over the past few decades, presenting a simple, yet efficient means of modelling and understanding complex systems. Networks are employed in various different areas, for instance, in the modelling of disease spread in human and animal contact networks. Networks also find applications in marketing, where various measures are used to recommend items to customers of, for instance, online shopping portals. Many other real world phenomena can be described and analysed using complex networks. Most scientific literature focuses on the analysis of, so called, one-mode networks. However, many systems are best represented as bipartite networks. A network is bipartite if its vertices can be partitioned into two disjoint sets, where interaction takes place solely between vertices belonging to different sets. For instance, the network of scientists and papers, resulting from collaborations, is bipartite, with connections only existing between authors and papers. Similarly, the network of actors and the movies in which they appear is bipartite. This thesis is motivated by the lack of network measures designed particularly for the analysis of bipartite networks. Since many one-mode network measures are not applicable to bipartite structures, often the only available path to analysing bipartite data is the examination of its projections. A projection converts a bipartite network into an ordinary one-mode network, causing loss of valuable information amongst other problems. We are interested in both the theoretical aspects of bipartite networks and the applications to real world data. Throughout this thesis we analyse several real world networks with the aim of uncovering significant behaviour. We take two different approaches to gain a better understanding of complex bipartite networks. First, we deal with the problems that arise from the projection of bipartite networks, with the aim of overcoming these. Second, we develop network measures that are designed especially for bipartite networks. Despite the many problems that arise from converting a bipartite network into a one-mode network, the study of projections is ubiquitous throughout the network science literature and projections are often preferred above the direct analysis of bipartite networks. The one-mode projection of a bipartite network is constructed by dropping one of its node sets and connecting two nodes of the remaining set if they share at least one neighbour in the bipartite network, leading to an inflation of edges in the projection. Furthermore, the indirect inference of edges between nodes in the one-mode projection leads to noise, that is, many edges with insignificant meaning are introduced. We develop a novel technique of identifying the significant connections that form the backbone of one-mode projections by considering the degree distributions of the bipartite network. We show that this identification of significant edges cannot be achieved by trivial methods such as an application of a threshold to the edge weights. Furthermore, we show that the weights of one-mode projections of real world bipartite networks follow a Poisson binomial distribution. Real world one-mode projections often have well hidden community structures. These structures can be uncovered by dropping insignificant connections, as identified by our technique. In addition, our technique allows a ranking of edges by importance. We apply this backbone technique to three different real world networks, and show that our method is a very efficient way of identifying communities within diverse networks, such as the political parties in a Facebook network of posts by candidates and user likes. The development of new network measures that can be applied directly to bipartite networks is a crucial step towards a better understanding of these structures. One of the most important and widely used network measures is the clustering coefficient. Due to the particular structure of bipartite networks, the clustering coefficient cannot be directly applied to them. Although several definitions for the bipartite clustering coefficient have been presented in the literature, they are inconsistent and hence we explore this topic in great depth. We identify different types of bipartite networks based on their development over time, consequently requiring different definitions of the bipartite clustering coefficient. We precisely define the different types of networks before providing new definitions of the clustering coefficients for each type of bipartite network. We apply our clustering coefficients to discover the most influential nodes in real world bipartite networks by introducing the notion of the driving score. The driving score indicates the extent to which each individual node contributes to the overall clustering behaviour of the network. Another application of our clustering coefficient is the prediction of the future popularity of new items in rating networks. We are able to considerably improve existing predictions. Crime networks form a very interesting group of bipartite networks. Knowledge about their dynamics is especially important for the implementation of efficient crime prevention measures. We present two case studies of crime networks revealing many interesting insights, by using a combination of both the approaches outlined above. For instance, our analysis reveals significant co-occurrences of illegal activity and identifies areas that exhibit similar crime dynamics. The calculation of many network measures, including the ones we introduce in this thesis, require the enumeration of sub-graphs. In the last chapter of this thesis, we investigate several efficient ways of enumerating sub-graphs in bipartite networks, by studying, combining and modifying existing algorithms. We also present preliminary work on the theoretical problem of path enumeration