On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of...On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of alot of cliques,which intensively connect and overlap with each other.We study the network properties,which includethe degree distribution,multiple edges' overlapping time distribution,distribution of the overlap size between any twooverlapping cliques,distribution of the number of cliques that a node belongs to.Naturally,the cliques also constitute anetwork,with the overlapping nodes being their multiple links.We also research its network properties such as degreedistribution,clustering,average path length,and so on.We propose that a BTN has the properties of random cliqueincrement and random overlapping clique,at the same time,a BTN is a small-world network with highly clique-clusteredand highly clique-overlapped.Finally,we introduce a BTN evolution model,whose simulation results agree well withthe statistical laws that emerge in real BTNs.展开更多
In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. ...In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.展开更多
Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m)...Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m),Γ (m)(E)∩Γ (m)(F) is studied.In particular,sizes of maximal cliques in Γ (m) are determined and it is shown that Γ (m) is not edge-regular when m<n-1.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos.60504027 and 60874080the Postdoctor Science Foundation of China under Grant No.20060401037
文摘On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of alot of cliques,which intensively connect and overlap with each other.We study the network properties,which includethe degree distribution,multiple edges' overlapping time distribution,distribution of the overlap size between any twooverlapping cliques,distribution of the number of cliques that a node belongs to.Naturally,the cliques also constitute anetwork,with the overlapping nodes being their multiple links.We also research its network properties such as degreedistribution,clustering,average path length,and so on.We propose that a BTN has the properties of random cliqueincrement and random overlapping clique,at the same time,a BTN is a small-world network with highly clique-clusteredand highly clique-overlapped.Finally,we introduce a BTN evolution model,whose simulation results agree well withthe statistical laws that emerge in real BTNs.
文摘In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.
基金Supported by the National Natural Science Foundation of China(1 95 71 0 2 4 ) and Hunan Provincial De-partmentof Education(0 2 C5 1 2 )
文摘Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m),Γ (m)(E)∩Γ (m)(F) is studied.In particular,sizes of maximal cliques in Γ (m) are determined and it is shown that Γ (m) is not edge-regular when m<n-1.
