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Many complex systems can be represented as networks, with vertices for individuals and edges denoting relations between them. The study of the structure and properties of a network can help to understand the behaviour of elements in the network in order to improve the productivity and quality of life of humans. This thesis aims at exploring the structure of complex networks and the impact of the structure on their behaviour. It is motivated by two problems in network analysis: community detection and edge prediction. In this thesis, we develop a series of techniques for predicting missing edges and detecting communities in complex networks. One of the significant findings is that some existing techniques in these two areas can be used in complementary ways. For example, missing edges are more likely to be found within communities than between different communities, and the community structure can be discovered by extra information on edges, for example, weights, by using the feature of vertex similarity. We also analysed the influence of different types of missing edges on network analysis methods. Another hypothesis is that a community can be defined as a clique with missing edges, inspired a new community detection algorithm. Finally, we extended a popular sampling method in epidemiology to allow the recovery of the structure, especially the community structure, of a network from samples. Another interesting finding is that we can even use key vertices found from samples to control the spread of an infection in the original network.

As one of the major fields, Networked Multi-Agent Systems (NMAS), which deals with the study of how network architecture and interactions among network components influence global control goals, has received wide attention across science and engineering. A usual problem that appears in the coordination of NMAS is the consensus problem, i.e., given initial values (scalar or vector) of agents, establish conditions under which through local interactions and computations, the agents asymptotically achieve some kind of agreement, such as control of mobile vehicles, information processing in sensor networks and design of distributed algorithms. Researches have mainly focused on the analysis of NMAS consensus in the past; the interconnection topology and some consensus algorithms were given in advance and the relevant research objective was to verify whether the states of all agents converge to some common value. Agents with single integrator dynamics, double integrator dynamics or more complicated dynamics are the present research emphasis. In addition, most present research activities focus on theoretical study of consensus problems based on relatively simple simulation experiments, but such method will still be a key element of research in the future. Although it is more complicated to consider consensus problems for a team of agents with more complex nonlinear dynamics and even heterogenous dynamics, such kind of problems are very important. To the best of our knowledge, there are few effective. results on this topic. Usually, no common equilibrium for all agents exists even if each isolated agent has an equilibrium, but NMAS with non-identical agents may still exhibit some consensus behaviors which are far from being fully understood. Certain reasonable and satisfactory boundedness of state motion errors between different agents can be taken as useful consensus properties. This thesis focuses on the global consensus problems of NMAS consisting of identical or non-identical agent dynamics, and the proposed consensus property is formulated in terms of certain boundedness of state errors. Moreover, in particular circumstances, we still investigate their exact consensus conditions. Compared with many existing results, the thesis makes several significant contributions. Firstly, we generalize the related results for the case of identical agent dynamics to the case of non-identical agent dynamics and the proposed results cover the existing criteria of networks with identical agent dynamics as special cases. Secondly, we consider the communication delay among the agents, global consensus criteria are given based on solving a number of lower dimensional matrix inequalities and scalar inequalities, which generalize the criteria using the method of the master stability function for NMAS with identical agents. Finally, globally bounded consensus conditions for both delay-independent and delay-dependent conditions based on the Lyapunov-Krasovskii functional method are derived.

The increasing adoption of sensor rich mobile devices supported by high-speed network connectivity has transformed our computing and communication environment. Context- aware services and applications are making their way into our daily lives. Physical spaces are now transforming into smart spaces with embedded services, thus bringing together the real and virtual worlds. These trends coupled with the unprecedented success of social networking websites have opened new vistas. Even though the social networking platform allows interaction amongst group of friends or contacts, it lacks in dynamically recognising potential group of users based on their physical activity or commonality, i.e. their context. Furthermore, they fail to leverage the multicast service delivery capabilities of the underlying communication networks. This thesis proposes a context aware group service delivery model called ambient multicast for a group of users, called ad-hoc communities, which are dynamically identified based on their context information. This work establishes its basis on the sociological and technical discussion of groups and their dynamics. The availability of context information acts as the bridge between the groups which exist in the real world and the more static virtual groups. Contextual changes over the course of time, result in continuous disintegration of existing groups and formation of new ones. An important challenge in supporting such ad-hoc communities is the availability of a generic context aware model, which is suitable for mobile users. This research proposes a broker- consumer-provider based context aware architecture which decouples the application logic from the context acquisition and dissemination model. The proposed architecture is based on service oriented architecture principles and supports gradual introduction of context providers and context consumers. The application development cycle is narrow because the context discovery, acquisition and aggregation complexity is hidden behind the broker component.

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