Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree...Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree distribution,but also the scaling clustering coefficient property which Barabási-Albert(BA)model does not have.BA model is a model of network growth based on growth and preferential attachment,showing the scale-free degree distribution property.In this paper,we study the evolution of cooperation on a hierarchical network model,adopting the prisoner's dilemma(PD)game and snowdrift game(SG)as metaphors of the interplay between connected nodes.BA model provides a unifying framework for the emergence of cooperation.But interestingly,we found that on hierarchical model,there is no sign of cooperation for PD game,while the fre-quency of cooperation decreases as the common benefit decreases for SG.By comparing the scaling clustering coefficient prop-erties of the hierarchical network model with that of BA model,we found that the former amplifies the effect of hubs.Considering different performances of PD game and SG on complex network,we also found that common benefit leads to cooperation in the evolution.Thus our study may shed light on the emergence of cooperation in both natural and social environments.展开更多
So far,the acyclic hypergraph has two different definitions.One is based on the cyclomatic number of the hypergraph,whereas the other arises from the acyclic schema of the relational database in the computer science.I...So far,the acyclic hypergraph has two different definitions.One is based on the cyclomatic number of the hypergraph,whereas the other arises from the acyclic schema of the relational database in the computer science.In this paper,it is first proved that these two definitions coincide with each other completely.Then we prove that a hypergraph H is not acyclic,or cyclic,if and only if it contains a special partial hypergraph named hypercircuit.In addition,we show that H has l(H) different hypercircuits,where l(H)is a parameter used to decide whether H is acyclic or cyclic.展开更多
基金Project supported by the Natural Science Foundation of ZhejiangProvince, China (No. Y105697)the Ningbo Natural ScienceFoundation,China (No. 2005A610004)
文摘Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree distribution,but also the scaling clustering coefficient property which Barabási-Albert(BA)model does not have.BA model is a model of network growth based on growth and preferential attachment,showing the scale-free degree distribution property.In this paper,we study the evolution of cooperation on a hierarchical network model,adopting the prisoner's dilemma(PD)game and snowdrift game(SG)as metaphors of the interplay between connected nodes.BA model provides a unifying framework for the emergence of cooperation.But interestingly,we found that on hierarchical model,there is no sign of cooperation for PD game,while the fre-quency of cooperation decreases as the common benefit decreases for SG.By comparing the scaling clustering coefficient prop-erties of the hierarchical network model with that of BA model,we found that the former amplifies the effect of hubs.Considering different performances of PD game and SG on complex network,we also found that common benefit leads to cooperation in the evolution.Thus our study may shed light on the emergence of cooperation in both natural and social environments.
基金This research is supported by the National Natural Science Foundation of China(No. 19831080).
文摘So far,the acyclic hypergraph has two different definitions.One is based on the cyclomatic number of the hypergraph,whereas the other arises from the acyclic schema of the relational database in the computer science.In this paper,it is first proved that these two definitions coincide with each other completely.Then we prove that a hypergraph H is not acyclic,or cyclic,if and only if it contains a special partial hypergraph named hypercircuit.In addition,we show that H has l(H) different hypercircuits,where l(H)is a parameter used to decide whether H is acyclic or cyclic.
