We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study th...We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.展开更多
Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs, Discrete Mathematics, 235, 2001, 245-253), we show that several well-known graph layout problems are appro...Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs, Discrete Mathematics, 235, 2001, 245-253), we show that several well-known graph layout problems are approximable to within a factor arbitrarily close to 1 of the optimal with high probability for random graphs drawn from an Erdös-Renyi distribution with appropriate sparsity conditions using only elementary probabilistic analysis. Moreover, we show that the same results hold for the analogous problems on directed acyclic graphs.展开更多
Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. This paper presents a specific realizatio...Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. This paper presents a specific realization of a class of random network models in which the connection probability between two vertices （i, j） is a specific function of degrees ki and kj. In the framework of the configuration model of random graphsp we find the analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The obtained expressions are checked by means of numerical simulations. Possible applications of our model are discussed.展开更多
Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of compl...Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.展开更多
This research studied the concept of enacted peer support during adolescence by means of the Harry Potter Series. A network approach was used. Results indicated the importance of reciprocity and transitivity for enact...This research studied the concept of enacted peer support during adolescence by means of the Harry Potter Series. A network approach was used. Results indicated the importance of reciprocity and transitivity for enacted peer support during adolescence. Contrary to our expectations, gender, age and personality traits did not affect enacted peer support. No homophily effects based on gender and age were detected. However, students were found to be more supportive of students with similar personality traits. We hope this study adds to the current knowledge on peer support in adolescence and promotes the use of social theories and methods in literacy research.展开更多
In this work we study virtual social networks known as Facebook. It is used by millions of people worldwide, gathering a combination of virtual elements and real world components. We suggest a probabilistic model to d...In this work we study virtual social networks known as Facebook. It is used by millions of people worldwide, gathering a combination of virtual elements and real world components. We suggest a probabilistic model to describe the long-term behavior of Facebook. This model includes different friendship connection between profiles, directly or by suggestion. Due to web’s high interactivity level, we simplify the model assuming Markovian dynamic. After the model is established we propose Complete Transversality (CT) communication concept. CT describes people interaction that reflects profile behaviour and leads to estimators that measure this interaction. Then we introduce a weakness version of CT named Segmental Transversality (ST). Within this framework we develop estimators that allow hypothesis testing of CT and ST. And then, in ST context we propose performance measures to address a priori segmentation’s quality.展开更多
Let N = （G, c） be a random electrical network obtained by assigning a certain resistance for each edge in a random graph G ∈ G（n, p） and the potentials on the boundary vertices. In this paper, we prove that with ...Let N = （G, c） be a random electrical network obtained by assigning a certain resistance for each edge in a random graph G ∈ G（n, p） and the potentials on the boundary vertices. In this paper, we prove that with high probability the potential distribution of all vertices of G is very close to a constant.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 70501032.
文摘We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.
文摘Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs, Discrete Mathematics, 235, 2001, 245-253), we show that several well-known graph layout problems are approximable to within a factor arbitrarily close to 1 of the optimal with high probability for random graphs drawn from an Erdös-Renyi distribution with appropriate sparsity conditions using only elementary probabilistic analysis. Moreover, we show that the same results hold for the analogous problems on directed acyclic graphs.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10375025 and 10275027） and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China （Grant No 704035）
文摘Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. This paper presents a specific realization of a class of random network models in which the connection probability between two vertices （i, j） is a specific function of degrees ki and kj. In the framework of the configuration model of random graphsp we find the analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The obtained expressions are checked by means of numerical simulations. Possible applications of our model are discussed.
基金Project supported by the Research Foundation from Ministry of Science and Technology, China （Grant Nos 2006AA02Z317,2004CB720103, 2003CB715901 and 2006AA02312）, the National High Technology Research and Development Program of China （Grant No 2006AA020805）, the National Natural Science Foundation of China （Grant Nos 30500107, 30670953 and 30670574）, the International Cooperation Project of Science and Technology Commission of Shanghai Municipality, China （Grant No 06RS07109）, and Grant from Science and Technology Commission of Shanghai Municipality, China （Grant Nos 04DZ19850, 06PJ14072 and 04DZ 14005）.Acknowledgement We thank Luis A. Nunes Amaral and Roger Guimerà for kindly providing us with the software Modul-w of computing the network modularity metric. Our gratitude must also be extended to John Doyle, Petter Holme and Lun Li for useful discussion and constructive comments.
文摘Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.
文摘This research studied the concept of enacted peer support during adolescence by means of the Harry Potter Series. A network approach was used. Results indicated the importance of reciprocity and transitivity for enacted peer support during adolescence. Contrary to our expectations, gender, age and personality traits did not affect enacted peer support. No homophily effects based on gender and age were detected. However, students were found to be more supportive of students with similar personality traits. We hope this study adds to the current knowledge on peer support in adolescence and promotes the use of social theories and methods in literacy research.
文摘In this work we study virtual social networks known as Facebook. It is used by millions of people worldwide, gathering a combination of virtual elements and real world components. We suggest a probabilistic model to describe the long-term behavior of Facebook. This model includes different friendship connection between profiles, directly or by suggestion. Due to web’s high interactivity level, we simplify the model assuming Markovian dynamic. After the model is established we propose Complete Transversality (CT) communication concept. CT describes people interaction that reflects profile behaviour and leads to estimators that measure this interaction. Then we introduce a weakness version of CT named Segmental Transversality (ST). Within this framework we develop estimators that allow hypothesis testing of CT and ST. And then, in ST context we propose performance measures to address a priori segmentation’s quality.
基金Supported by the National Natural Science Foundation of China (No.10531070 and 1091137)National Basic Research Program of China 973 Program (No. 2006CB805900)a grant of Science and Technology Commission of Shanghai Municipality (STCSM, No. 09XD1402500)
文摘Let N = （G, c） be a random electrical network obtained by assigning a certain resistance for each edge in a random graph G ∈ G（n, p） and the potentials on the boundary vertices. In this paper, we prove that with high probability the potential distribution of all vertices of G is very close to a constant.
基金Supported by National Natural Science Foundation of China(10971137)National Key Basic Research(973)Program of China(2006CB805900)a grant from Science and Technology Commission of Shanghai Municipality(09XD1402500)
