Research Of Spreading Properties On Several Models Of Complex Networks

The research of complex networks has penetrated into many different fields includingMathematical and Physical Sciences, Life Sciences and Engineering Sciences and has become ahot research topic in recent years. There are two important research directions in complexnetworks----network models and spreading properties on networks. In the past few years,researchers have carried out considerable studies on the two directions and proposed manypractical network models and spreading models. Although fruitful achievements have been made,many problems are still to be studied and solved. In this paper, complex network models andspreading properties on networks are studied by using statistical physics, operational researchand computer simulation. The main contents and originalities of this paper can be summarized asfollows:1. Studing the rumor spreading properties on the local-world networkRumor is a very universal phenomenon in real society and its effect cannot beunderestimated in emergency and many crises. A local-world is a ubiquitous structure in manyrealistic networks. For example, in the World Trade Web, many countries emphatically acceleratetheir economy collaborations in various regional economy cooperative organizations (such as theEuropean Union, Association of Southeast Asian Nations, North America Free Trade Area, etc).And in human social, in fact everyone lives in the local-world of their own and has their owncircle of friends. The rumor spreading properties on the local-world network are studied by usingtwo indexes which measure the rumor spreading ability. The results indicate that the local-worldscale and the immune probability both play important roles in rumor propagation under the fixedtransmission probability.2. Proposing a new information spreading model with preference and studing the spreadingproperties on small-world networks and scale-free networksPreference is very important and decisions are usually based on the personal preference. For the same information offered by a certain friend, some people are interested in it and are willingto spread it, but some people are not interested in it and are not willing to spread it. That is to say,whether people are interested in and propagate the information depends on their preferences,while the extent can be quantified by using the utility function value. In this paper the utilityfunction is introduced to the information dissemination and a new information spreading modelwith preference is put forward. The information spreading properties on small-world networksand scale-free networks are studied by computer simulation. The relationship between the utilityvalue and the information spreading ability is revealed mainly.3. Proposing three new epidemic spreading models and studing the spreading properties onsmall-world networks and scale-free networksIn real epidemiology, the immunity of removed individual is different. Some removedindividuals will lose all the immunity and become susceptible individuals, but some removedindividuals will retain partial immunity (i.e., weakened immunity) and become lowersusceptible individuals. A lower susceptible individual will not be infected immediately if itmakes contact with infected individuals. It just loses the partial immunity and becomessusceptible individual. First of all, based on this mechanism of infection, a new practicalepidemic spreading model—epidemic model with lower susceptibility (i.e., SIRSLS model) isproposed. The epidemic threshold of this model on small-world networks and scale-freenetworks are deduced by using the mean field method. There exists a nonzero epidemicthreshold on small-world networks and the threshold is null if the size of scale-free networks issufficiently large. For another, in the process of epidemic spreading, each individual will notcontact all its neighbors once at each time step. Thus supposed that every individual has thesame infectivity, two new epidemic spreading models—SIRS model with identical infectivityand SIRSLS model with identical infectivity are proposed. The epidemic thresholds of the twomodels on scale-free networks are deduced through the mean field method. Different formSIRSLS model, the thresholds of the two models are nonzero even if the size of scale-freenetworks is sufficiently large. Through the computer simulation research on epidemic spreadingprocess, we find that the theoretical results and the simulation results are in good agreement.4. Proposing a new weighted local-world network evolving model based on the edgepreferential selection and studing the epidemic spreading properties on this network Complex network model is an abstract object to simulate and study realistic networkswhich including unweighted network model and weighted network model. In the unweightednetwork model, only the existence of edges between nodes is showed, but the important of eachedge is known as identical. It is not correspond exactly to the realistic networks. For instance, inthe scientific collaboration network, even with the cooperation relations, the number ofcoauthored publications of different parters is unequal and in the airline transportation network,even with the airport, the passenger capacity on this route between different airports is alsounequal. So, it is better to describe some real networks by using the weighted networks. Theintensive collaborations have a greater chance to attract new collaborators than occasionalconnections in the scientific collaboration network. In other words, it is the edge but not nodethat attracts new links. Therefore, based on this phenomenon, a new weighted local-networkmodel based on the edge preferential selection is proposed. The weight distribution, the strengthdistribution and the degree distribution of this model are deduced by using the mean fieldmethod. All results of the computer simulation are well consistent with the analytical results.What’s more important is that the weight dynamics of the new model can simulate somerealistic networks such as Neural network of the nematode C. Elegans and Online SocialNetwork. Finally the epidemic spreading properties on this new network are analyzed.