Identifying influential nodes in complex networks: Effective distance gravity model

The identification of important nodes in complex networks is an area of exciting growth due to its applications across various disciplines like disease controlling, community finding, data mining, network system controlling, just to name a few. Many measures have thus been proposed to date, and these measures are either based on the locality of nodes or the global nature of the network. These measures typically use distance based on the concept of traditional Euclidean Distance, which only focus on the local static geographic distance between nodes but ignore the interaction between nodes in real-world networks. However, a variety of factors should be considered for the purpose of identifying influential nodes, such as degree, edge, direction and weight. Some methods based on evidence theory have also been proposed. In this paper, we have proposed an original and novel gravity model with effective distance for identifying influential nodes based on information fusion and multi-level processing. Our method is able to comprehensively consider the global and local information of the complex network, and also utilize the effective distance to replace the Euclidean Distance. This allows us to fully consider the complex topological structure of the real network, as well as the dynamic interaction information between nodes. In order to validate the effectiveness of our proposed method, we have utilized the susceptible infected (SI) model to carry out a variety of simulations on eight different real-world networks using six existing well-known methods. The experimental results indicate the reasonableness and effectiveness of our proposed method

The network asymmetry caused by the degree correlation and its effect on the bimodality in control

Our ability to control a whole network can be achieved via a small set of driver nodes. While the minimum number of driver nodes needed for control is fixed in a given network, there are multiple choices for the driver node set. A quantity used to investigate this multiplicity is the fraction of redundant nodes in the network, referring to nodes that do not need any external control. Previous work has discovered a bimodality feature characterized by a bifurcation diagram: networks with the same statistical property would stay with equal probability to have a large or small fraction of redundant nodes. Here we find that this feature is rooted in the symmetry of the directed network, where both the degree distribution and the degree correlation can play a role. The in-in and out-out degree correlation will suppress the bifurcation, as networks with such degree correlations are asymmetric under network transpose. The out-in and in-out degree correlation do not change the network symmetry, hence the bimodality feature is preserved. However, the out-in degree correlation will change the critical average degree needed for the bifurcation. Hence by fixing the average degree of networks and tuning out-in degree correlation alone, we can observe a similar bifurcation diagram. We conduct analytical analyses that adequately explain the emergence of bimodality caused by out-in degree correlation. We also propose a quantity, taking both degree distribution and degree correlation into consideration, to predict if a network would be at the upper or lower branch of the bifurcation. As is well known that most real networks are not neutral, our results extend our understandings of the controllability of complex networks.Comment: 25 pages, 8 figures, to be published in Physica A: Statistical Mechanics and its Application