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Although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function, a unified definition of the heterogeneity of a network with any degree distribution is absent. In this paper, we define a heterogeneity index 0≤H<1 to quantify the degree heterogeneity of any given network. We analytically show the existence of an...
We investigate the distribution of vertex overpayments in a kind of power-law networks when the degree distribution exponent is varied from 2 to infin . The overpayment of one vertex is the sum of the increase of shortest path lengths among all pairs of vertices in the network if the vertex were deleted. We find the overpayment increases with degree in the power-law form not only in heterogeneous...
Using a rewiring-edge method without changing the degree distribution of a network, we propose a weighted homogeneous small-world (HOSW) network model in which all nodes have the same degree. It is found that with the increase of the rewiring probability, which is defined as the ratio of the number of rewiring edges to the total edges in the network, both the average clustering and average path length...
In this paper, an edge rewiring mechanism is proposed to optimize the synchronizability of a power law network with keeping the degree of each vertex unchanged, and the network synchronizability after the novel optimal rewiring is enhanced. The rewiring mechanism is also found to reduce the characteristic path length and maximum betweenness centrality of the network
The history and current research of consensus problem are reviewed, including consensus protocols and convergence analysis techniques, connection between consensus schemes and other control paradigms, and applications. Several major advanced problems are presented such as consensus problem in complex networks, consensus filters in sensor networks. Some related problems such as synchronization, formation...
This paper investigate consensus problems in an extended scale-free network model. It is found that as the network becomes more homogeneous, the convergence speed decreased; however, the maximal tolerate delay time of the network achieving consensus is increased. Therefore, there is a trade-off between the speed of achieving consensus and the robust to the delay time.
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