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The one-mode projecting is extensively used to compress the bipartite networks. Since the one-mode projection is always less informative than the bipartite representation, a proper weighting method is required to better retain the original information. In this article, inspired by the network-based resource-allocation dynamics, we raise a weighting method, which can be directly applied in extracting the hidden information of networks, with remarkably better performance than the widely used global ranking method as well as collaborative filtering. This work not only provides a creditable method in compressing bipartite networks, but also highlights a possible way for the better solution of a long-standing challenge in modern information science: How to do personal recommendation?
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It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations.
This letter propose a new model for characterizing traffic dynamics in scale-free networks. With a replotted road map of cities with roads mapped to vertices and intersections to edges, and introducing the road capacity L and its handling ability at intersections C, the model can be applied to urban traffic system. Simulations give the overall capacity of the traffic system which is quantified by a phase transition from free flow to congestion. Moreover, we report the fundamental diagram of flow against density, in which hysteresis is found, indicating that the system is bistable in a certain range of vehicle density. In addition, the fundamental diagram is significantly different from single-lane traffic model and 2-D BML model with four states: free flow, saturated flow, bistable and jammed.
Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications and usually allow for analyticity. There lacks a quantity, however, to tell the ratio of cycles which determines the extent of network being close to tree networks. Therefore we introduce the term Cycle Nodes Ratio (CNR) to describe the ratio of number of nodes belonging to cycles to the number of total nodes, and provide an algorithm to calculate CNR. CNR is studied in both network models and real networks. The CNR remains unchanged in different sized Erdos Renyi (ER) networks with the same average degree, and increases with the average degree, which yields a critical turning point. The approximate analytical solutions of CNR in ER networks are given, which fits the simulations well. Furthermore, the difference between CNR and two-core ratio (TCR) is analyzed. The critical phenomenon is explored by analysing the giant component of networks. We compare the CNR in network models and real networks, and find the latter is generally smaller. Combining the coarse-graining method can distinguish the CNR structure of networks with high average degree. The CNR is also applied to four different kinds of transportation networks and fungal networks, which give rise to different zones of effect. It is interesting to see that CNR is very useful in network recognition of machine learning.
This paper presents an evolution model of weighted networks in which the structural growth and weight dynamics are driven by human behavior, i.e. passenger route choice behavior. Transportation networks grow due to peoples increasing travel demand and the pattern of growth is determined by their route choice behavior. In airline networks passengers often transfer from a third airport instead of flying directly to the destination, which contributes to the hubs formation and finally the scale-free statistical property. In this model we assume at each time step there emerges a new node with m travel destinations. Then the new node either connects destination directly with the probability p or transfers from a third node with the probability 1-p. The analytical result shows degree and strength both obey power-law distribution with the exponent between 2.33 and 3 depending on p. The weights also obey power-law distribution. The clustering coefficient, degree assortatively coefficient and degree-strength correlation are all dependent on the probability p. This model can also be used in social networks.
Networks representing complex systems in nature and society usually involve multiple interaction types. These types suggest essential information on the interactions between components, but not all of the existing types are usually discovered. Therefore, detecting the undiscovered edge types is crucial for deepening our understanding of the network structure. Although previous studies have discussed the edge label detection problem, we still lack effective methods for uncovering previously-undetected edge types. Here, we develop an effective technique to detect undiscovered new edge types in networks by leveraging a novel temporal network model. Both analytical and numerical results show that the prediction accuracy of our method is perfect when the model networks time parameter approaches infinity. Furthermore, we find that when time is finite, our method is still significantly more accurate than the baseline.
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