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Recently, we introduced a quantity, node weight, to describe the collaboration sharing or competition gain of the elements in the collaboration-competition networks, which can be well described by bipartite graphs. We find that the node weight distributions of all the networks follow the so-called shifted power law (SPL). The common distribution function may indicate that the evolution of the collaboration and competition in very different systems obeys a general rule. In order to set up a base of the further investigations on the universal system evolution dynamics, we now present the definition of the networks and their node weights, the node weight distributions, as well as the evolution durations of 15 real world collaboration-competition systems which are belonging to diverse fields.
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Recently, our group quantitatively defined two quantities, competition ability and uniqueness (Chin. Phys. Lett. 26 (2009) 058901) for a kind of cooperation-competition bipartite networks, where producers produce some products and output them to a market to make competition. Factories, universities or restaurants can serve as the examples. In the letter we presented an analytical conclusion that the competition ability was linearly dependent on the uniqueness in the trivial cases, where both the input quality and competition gain obey normal distributions. The competition between Chinese regional universities was taken as examples. In this article we discuss the abnormal cases where competition gains show the distributions near to power laws. In addition, we extend the study onto all the cooperation-competition bipartite networks and therefore redefine the competition ability. The empirical investigation of the competition ability dependence on the uniqueness in 15 real world collaboration-competition systems is presented, 14 of which belong to the general nontrivial cases. We find that the dependence generally follows the so-called shifted power law (SPL), but very near to power laws. The empirically obtained heterogeneity indexes of the distributions of competition ability and uniqueness are also presented. These empirical investigations will be used as a supplementary of a future paper, which will present the comparison and further discussions about the competition ability dependence on the uniqueness in the abnormal collaboration-competition systems and the relationship between the dependence and the competition ability and uniqueness heterogeneity.
Competition and collaboration are at the heart of multi-agent probabilistic spreading processes. The battle on public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple diseases such as HIV and tuberculosis demonstrates the latter. These spreads are influenced by the underlying network topology, the infection rates between network constituents, recovery rates and, equally importantly, the interactions between the spreading processes themselves. Here, for the first time we derive dynamic message-passing equations that provide an exact description of the dynamics of two interacting spreading processes on tree graphs, and develop systematic low-complexity models that predict the spread on general graphs. We also develop a theoretical framework for an optimal control of interacting spreading processes through an optimized resource allocation under budget constraints and within a finite time window. Derived algorithms can be used to maximize the desired spread in the presence of a rival competitive process, and to limit the spread through vaccination in the case of coupled infectious diseases. We demonstrate the efficacy of the framework and optimization method on both synthetic and real-world networks.
Bipartite matching problem is to study two disjoint groups of agents who need to be matched pairwise. It can be applied to many real-world scenarios and explain many social phenomena. In this article, we study the effect of competition on bipartite matching problem by introducing correlated wish list. The results show that proper competition can improve the overall happiness of society and also reduce the instability of the matching result of unequal sized bipartite matching.
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.
We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the co-authorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Rand index and of the adjusted Wallace index respectively. The detection of cores is highly precise although the accuracy of the methodology can be limited in some cases.
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