The control of complex networks is affected by their structural characteristic. As a type of key nodes in a network structure, cut vertexes are essential for network connectivity because their removal will disconnect ...The control of complex networks is affected by their structural characteristic. As a type of key nodes in a network structure, cut vertexes are essential for network connectivity because their removal will disconnect the network. Despite their fundamental importance, the influence of the cut vertexes on network control is still uncertain. Here, we reveal the relationship between the cut vertexes and the driver nodes, and find that the driver nodes tend to avoid the cut vertexes.However, driving cut vertexes reduce the energy required for controlling complex networks, since cut vertexes are located near the middle of the control chains. By employing three different node failure strategies, we investigate the impact of cut vertexes failure on the energy required. The results show that cut vertex failures markedly increase the control energy because the cut vertexes are larger-degree nodes. Our results deepen the understanding of the structural characteristic in network control.展开更多
Let ψ be a certain set of graphs.A graph is called a minimizing graph in the set ψ if its least eigenvalue attains the minimum among all graphs in ψ.In this paper,we determine the unique minimizing graph in ψn,whe...Let ψ be a certain set of graphs.A graph is called a minimizing graph in the set ψ if its least eigenvalue attains the minimum among all graphs in ψ.In this paper,we determine the unique minimizing graph in ψn,where ψn denotes the set of connected graphs of order n with cut vertices.展开更多
Evidence shows that biological systems are composed of separable functional modules. Identifying protein complexes is essential for understanding the principles of cellular functions. Many methods have been proposed t...Evidence shows that biological systems are composed of separable functional modules. Identifying protein complexes is essential for understanding the principles of cellular functions. Many methods have been proposed to mine protein complexes from protein-protein interaction networks. However, the performances of these algorithms are not good enough since the protein-protein interactions detected from experiments are not complete and have noise. This paper presents an analysis of the topological properties of protein complexes to show that although proteins from the same complex are more highly connected than proteins from different complexes, many protein complexes are not very dense (density ≥0.8). A method is then given to mine protein complexes that are relatively dense (density ≥0.4). In the first step, a topology property is used to identify proteins that are probably in a same complex. Then, a possible boundary is calculated based on a minimum vertex cut for the protein complex. The final complex is formed by the proteins within the boundary. The method is validated on a yeast protein-protein interaction network. The results show that this method has better performance in terms of sensitivity and specificity compared with other methods. The functional consistency is also good.展开更多
Let G(n,k,t) be a set of graphs with n vertices,k cut edges and t cut vertices.In this paper,we classify these graphs in G(n,k,t) according to cut vertices,and characterize the extremal graphs with the largest spe...Let G(n,k,t) be a set of graphs with n vertices,k cut edges and t cut vertices.In this paper,we classify these graphs in G(n,k,t) according to cut vertices,and characterize the extremal graphs with the largest spectral radius in G(n,k,t).展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 61763013)the Natural Science Foundation of Jiangxi Province of China (Grant No. 20202BABL212008)+1 种基金the Jiangxi Provincial Postdoctoral Preferred Project of China (Grant No. 2017KY37)the Key Research and Development Project of Jiangxi Province of China (Grant No. 20202BBEL53018)。
文摘The control of complex networks is affected by their structural characteristic. As a type of key nodes in a network structure, cut vertexes are essential for network connectivity because their removal will disconnect the network. Despite their fundamental importance, the influence of the cut vertexes on network control is still uncertain. Here, we reveal the relationship between the cut vertexes and the driver nodes, and find that the driver nodes tend to avoid the cut vertexes.However, driving cut vertexes reduce the energy required for controlling complex networks, since cut vertexes are located near the middle of the control chains. By employing three different node failure strategies, we investigate the impact of cut vertexes failure on the energy required. The results show that cut vertex failures markedly increase the control energy because the cut vertexes are larger-degree nodes. Our results deepen the understanding of the structural characteristic in network control.
基金Supported by the Supported by the National Natural Science Foundation of China (Grant No. 11071002)Key Project of Chinese Ministry of Education (Grant No. 210091)+4 种基金Anhui Provincial Natural Science Foundation(Grant No. 10040606Y33)Anhui University Innovation Team Project (Grant No. KJTD001B)Project of Anhui Province for Young Teachers Research Support in Universities (Grant No. 2008JQl021)Project of Anhui Province for Excellent Young Talents in Universities (Grant No. 2009SQRZ017ZD)the Natural Science Foundation of Department of Education of Anhui Province (Grant No. KJ2010B136)
文摘Let ψ be a certain set of graphs.A graph is called a minimizing graph in the set ψ if its least eigenvalue attains the minimum among all graphs in ψ.In this paper,we determine the unique minimizing graph in ψn,where ψn denotes the set of connected graphs of order n with cut vertices.
基金Supported in part by the National Natural Science Foundation of China (Nos.61232001 and 61073036)
文摘Evidence shows that biological systems are composed of separable functional modules. Identifying protein complexes is essential for understanding the principles of cellular functions. Many methods have been proposed to mine protein complexes from protein-protein interaction networks. However, the performances of these algorithms are not good enough since the protein-protein interactions detected from experiments are not complete and have noise. This paper presents an analysis of the topological properties of protein complexes to show that although proteins from the same complex are more highly connected than proteins from different complexes, many protein complexes are not very dense (density ≥0.8). A method is then given to mine protein complexes that are relatively dense (density ≥0.4). In the first step, a topology property is used to identify proteins that are probably in a same complex. Then, a possible boundary is calculated based on a minimum vertex cut for the protein complex. The final complex is formed by the proteins within the boundary. The method is validated on a yeast protein-protein interaction network. The results show that this method has better performance in terms of sensitivity and specificity compared with other methods. The functional consistency is also good.
基金Supported by National Natural Science Foundation of China(Grant No.11071078)
文摘Let G(n,k,t) be a set of graphs with n vertices,k cut edges and t cut vertices.In this paper,we classify these graphs in G(n,k,t) according to cut vertices,and characterize the extremal graphs with the largest spectral radius in G(n,k,t).