Studies On Structural And Dynamical Properties Of Complex Networks

Complex network exists in both nature and human society, such as transporta-tion networks, power systems, telephone communication networks, neural networks,cell networks, protein-protein interaction networks, Internet. Therefore, the study ofcomplex networks is of great significance for human life and work, and for the under-standing of evolution of nature.We present K-means approach and similarity measures to detect community dy-namic and infer community structure with other common algorithm. The modularitymeasures the quality of the clustering by inspecting the arrangement of the edges withinthe communities of vertices. We have provided algorithms for approximate computa-tion for nodes in different types of graphs, and have demonstrated the embedding onavailable dolphin dateset. A high modularity is an important indicator that the edgeswithin the communities outnumber (or have higher weights than) those in a similarrandomly generated graph (that does not present a community structure). Communitiesdiscovered using modularity optimization have a structure that is similar to the structureof cliques.Gossip spreading with four states ("Ignorant","Spreader","Stifler" and "Death")in social networks is showed in chapter3. We extend the standard model of gossip dis-semination, and give a complete simulation in BA networks under different conditions.Similarity measure of user rating play a positive information filter in social net-works is studied in chapter4. In the past decade, social recommending systems haveattracted increasing attention from the physical, social and computer science communi-ties. In this study, we use social networks to capture similarities of users’ interest and,accordingly, recommending systems to explore latent similarities. We build similarity-ratings-prediction models for a dataset of books and reviewers from Douban.com. Us-ing singular value decomposition, we evaluate the strengths and the weaknesses of thesimilarity measure, and discuss their effectiveness in recommending systems.We propose and study a minimal model of opinion dynamics on small world net-works. In particular, we reformulate the Hegselmann-Krause model as an interactivestochastic process and analyze it by means of computer simulations. We introduce self-coefficients in order to determine the impact of persistent players on the emergence ofconsensus. Depending on the fraction of directed long-range connections and the valueof self-coefficients, we observe fascinatingly rich dynamical behavior and transitions from disordered to ordered states. In general, we find that self-coefficients promote theemergence of consensus due to the so-called “group effect” that facilitates coalescencebetween otherwise separated network components. Since players want to maintain theirself-coefficients they are also behaviorally constrained, which may in turn impede fullconsensus. Sufficiently frequent long-range links are in such situations crucial for thenetwork to converge into an absorbing phase.