Rather than being randomly wired together, the components of complex network systems are recently reported to represent a scale-free architecture, in which the node degree distribution follows power-law. While social networks are scale-free, it is natural to utilize their structural properties in some social network applications. As a result, this dissertation explores social network architectures, and in turn, leverages these architectures to facilitate some influence and information propagation applications. Social network architectures are analyzed in two different aspects. The first aspect focuses on the node degree snowballing effects (i.e., degree growth effects) in social networks, which is based on an age-sensitive preferential attachment model. The impact of the initial links is explored, in terms of accelerating the node degree snowballing effects. The second aspect focuses on Nested Scale-Free Architectures (NSFAs) for social networks. The scale-free architecture is a classic concept, which means that the node degree distribution follows the power-law distribution. `Nested' indicates that the scale-free architecture is preserved when low-degree nodes and their associated connections are iteratively removed. NSFA has a bounded hierarchy. Based on the social network structure, this dissertation explores two influence propagation applications for the Social Influence Maximization Problem (SIMP). The first application is a friend recommendation strategy with the perspective of social influence maximization. For the system provider, the objective is to recommend a fixed number of new friends to a given user, such that the given user can maximize his/her social influence through making new friends. This problem is proved to be NP-hard by reduction from the SIMP. A greedy friend recommendation algorithm with an approximation ratio of $1-e^{-1}$ is proposed. The second application studies the SIMP with the crowd influence, which is NP-hard, monotone, non-submodular, and inapproximable in general graphs. However, since user connections in Online Social Networks (OSNs) are not random, approximations can be obtained by leveraging the structural properties of OSNs. The modularity, denoted by $\Delta$, is proposed to measure to what degree this problem violates the submodularity. Two approximation algorithms are proposed with ratios of $\frac{1}{\Delta+2}$ and $1-e^{-1/(\Delta+1)}$, respectively. Beside the influence propagation applications, this dissertation further explores three different information propagation applications. The first application is a social network quarantine strategy, which can eliminate epidemic outbreaks with minimal isolation costs. This problem is NP-hard. An approximation algorithm with a ratio of 2 is proposed through utilizing the problem properties of feasibility and minimality. The second application is a rating prediction scheme, called DynFluid, based on the fluid dynamics. DynFluid analogizes the rating reference among the users in OSNs to the fluid flow among containers. The third application is an information cascade prediction framework: given the social current cascade and social topology, the number of propagated users at a future time slot is predicted. To reduce prediction time complexities, the spatiotemporal cascade information (a larger size of data) is decomposed to user characteristics (a smaller size of data) for subsequent predictions. All these three applications are based on the social network structure. / Computer and Information Science

Empirical studies show that similar patterns emerge from a large number of different biological systems. For example, the group size distributions of several fish species and house sparrows all follow power law distributions with an exponential truncation. Networks built by ant colonies, slime mold and those are designed by engineers resemble each other in terms of structure and transportation efficiency. Based on the investigation of experimental data, we propose a variety of simple stochastic models to unravel the underlying mechanisms which lead to the collective phenomena in different systems. All the mechanisms employed in these models are rooted in the concept of selective reinforcement. In some systems the reinforcement can build optimal solutions for biological problem solving. This thesis consists of five papers. In the first three papers, I collaborate with biologists to look into group formation in house sparrows  and the movement decisions of damsel fish.  In the last two articles, I look at how shortest paths and networks are  constructed by slime molds and pheromone laying ants, as well as studying  speed-accuracy tradeoffs in slime molds' decision making. The general goal of the study is to better understand how macro level patterns and behaviors emerges from micro level interactions in both spatial and non-spatial biological systems. With the combination of mathematical modeling and experimentation, we are able to reproduce the macro level patterns in the studied biological systems and predict behaviors of the systems using minimum number of parameters.

Real-world large-scale complex networks such as the Internet, social networks and biological networks have increasingly attracted the interest of researchers from many areas. Accurate modelling of the statistical regularities of these large-scale networks is critical to understand their global evolving structures and local dynamical patterns. Traditionally, the Erdos and Renyi random graph model has helped the investigation of various homogeneous networks. During the past decade, a special computational methodology has emerged to study complex networks, the outcome of which is identified by two models: the Watts and Strogatz small-world model and the Barabasi-Albert scale-free model. At the core of the complex network modelling process is the extraction of characteristics of real-world networks. I have developed computer simulation algorithms for study of the properties of current theoretical models as well as for the measurement of two real-world complex networks, which lead to the isolation of three complex network modelling essentials. The main contribution of the thesis is the introduction and study of a new General Two-Stage growth model (GTS Model), which aims to describe and analyze many common-featured real-world complex networks. The tools we use to create the model and later perform many measurements on it consist of computer simulations, numerical analysis and mathematical derivations. In particular, two major cases of this GTS model have been studied. One is named the U-P model, which employs a new functional form of the network growth rule: a linear combination of preferential attachment and uniform attachment. The degree distribution of the model is first studied by computer simulation, while the exact solution is also obtained analytically. Two other important properties of complex networks: the characteristic path length and the clustering coefficient are also extensively investigated, obtaining either analytically derived solutions or numerical results by computer simulations. Furthermore, I demonstrate that the hub-hub interaction behaves in effect as the link between a network's topology and resilience property. The other is called the Hybrid model, which incorporates two stages of growth and studies the transition behaviour between the Erdos and Renyi random graph model and the Barabasi-Albert scale-free model. The Hybrid model is measured by extensive numerical simulations focusing on its degree distribution, characteristic path length and clustering coefficient. Although either of the two cases serves as a new approach to modelling real-world large-scale complex networks, perhaps more importantly, the general two-stage model provides a new theoretical framework for complex network modelling, which can be extended in many ways besides the two studied in this thesis.