Measuring centrality in a social network, especially in bipartite mode, poses many challenges, for example, the requirement of full knowledge of the network topology, and the lack of properly detecting top-k behavioral representative users. To overcome the above mentioned challenges, we propose HellRank, an accurate centrality measure for identifying central nodes in bipartite social networks. HellRank is based on the Hellinger distance between two nodes on the same side of a bipartite network. We theoretically analyze the impact of this distance on a bipartite network and find upper and lower bounds for it. The computation of the HellRank centrality measure can be distributed, by letting each node uses local information only on its immediate neighbors. Consequently, one does not need a central entity that has full knowledge of the network topological structure. We experimentally evaluate the performance of the HellRank measure in correlation with other centrality measures on real-world networks. The results show partial ranking similarity between the HellRank and the other conventional metrics according to the Kendall and Spearman rank correlation coefficient.
In the specific area of identifying influential users in bipartite networks, @cite_61 presented a dynamical model for rewiring in bipartite networks and obtained time-dependent degree distributions. @cite_31 defined a bipartite clustering coefficient by taking differently structured clusters into account, that can find important nodes across communities. The concept of clustering coefficient will be discussed in further detail in the Section .
@cite_61 @cite_31
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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. We describe a methodology to examine bipartite relational data structures as exemplified in networks of corporate interlocking. These structures can be represented as bipartite graphs of directors and companies, but direct comparison of empirical datasets is often problematic because graphs have different numbers of nodes and different densities. We compare empirical bipartite graphs to simulated random graph distributions conditional on constraints implicit in the observed datasets. We examine bipartite graphs directly, rather than simply converting them to two 1-mode graphs, allowing investigation of bipartite statistics important to connection redundancy and bipartite connectivity. We introduce a new bipartite clustering coefficient that measures tendencies for localized bipartite cycles. This coefficient can be interpreted as an indicator of inter-company and inter-director closenesss but high levels of bipartite clustering have a cost for long range connectivity. We also investigate degree distributions, path lengths, and counts of localized subgraphs. Using this new approach, we compare global structural properties of US and Australian interlocking company directors. By comparing observed statistics against those from the simulations, we assess how the observed graphs are structured, and make comparisons between them relative to the simulated graph distributions. We conclude that the two networks share many similarities and some differences. Notably, both structures tend to be influenced by the clustering of directors on boards, more than by the accumulation of board seats by individual directorss that shared multiple board memberships (multiple interlocks) are an important feature of both infrastructures, detracting from global connectivity (but more so in the Australian case)s and that company structural power may be relatively more diffuse in the US structure than in Australia. We present a dynamical model for rewiring and attachment in bipartite networks. Edges are placed between nodes that belong to catalogs that can either be fixed in size or growing in size. The model is motivated by an empirical study of data from the video rental service Netflix, which invites its users to give ratings to the videos available in its catalog. We find that the distribution of the number of ratings given by users and that of the number of ratings received by videos both follow a power law with an exponential cutoff. We also examine the activity patterns of Netflix users and find bursts of intense video-rating activity followed by long periods of inactivity. We derive ordinary differential equations to model the acquisition of edges by the nodes over time and obtain the corresponding time-dependent degree distributions. We then compare our results with the Netflix data and find good agreement. We conclude with a discussion of how catalog models can be used to study systems in which agents are ... A bipartite graph models the relation between two different types of entities. It is applicable, for example, to describe persons' affiliations to different social groups or their association with subjects such as topics of interest. In these applications, it is important to understand the connectivity patterns among the entities in the bipartite graph. For the example of a bipartite relation between persons and their topics of interest, people may form groups based on their common interests, and the topics also can be grouped or categorized based on the interested audiences. Co-clustering methods can identify such connectivity patterns and find clusters within the two types of entities simultaneously. In this paper, we propose an interactive visualization design that incorporates co-clustering methods to facilitate the identification of node clusters formed by their common connections in a bipartite graph. Besides highlighting the automatically detected node clusters and the connections among them, the visual interface also provides visual cues for evaluating the homogeneity of the bipartite connections in a cluster, identifying potential outliers, and analyzing the correlation of node attributes with the cluster structure. The interactive visual interface allows users to flexibly adjust the node grouping to incorporate their prior knowledge of the domain, either by direct manipulation (i.e., splitting and merging the clusters), or by providing explicit feedback on the cluster quality, based on which the system will learn a parametrization of the co-clustering algorithm to better align with the users' notion of node similarity. To demonstrate the utility of the system, we present two example usage scenarios on real world datasets.