Global Network Prediction from Local Node Dynamics

The study of dynamical systems on networks, describing complex interactive processes, provides insight into how network structure affects global behaviour. Yet many methods for network dynamics fail to cope with large or partially-known networks, a ubiquitous situation in real-world applications. Here we propose a localised method, applicable to a broad class of dynamical models on networks, whereby individual nodes monitor and store the evolution of their own state and use these values to approximate, via a simple computation, their own steady state solution. Hence the nodes predict their own final state without actually reaching it. Furthermore, the localised formulation enables nodes to compute global network metrics without knowledge of the full network structure. The method can be used to compute global rankings in the network from local information; to detect community detection from fast, local transient dynamics; and to identify key nodes that compute global network metrics ahead of others. We illustrate some of the applications of the algorithm by efficiently performing web-page ranking for a large internet network and identifying the dynamic roles of inter-neurons in the C. Elegans neural network. The mathematical formulation is simple, widely applicable and easily scalable to real-world datasets suggesting how local computation can provide an approach to the study of large-scale network dynamics

Prediction and modelling of complex social networks and their evolution.

This thesis focuses on complex social networks in the context of computational approaches for their prediction and modelling. The increasing popularity and advancement of social net- works paired with the availability of social network data enable empirical analysis, inference, prediction and modelling of social patterns. This data-driven approach towards social science is continuously evolving and is crucial for modelling and understanding of human social behaviour including predicting future social interactions for a wide range of applications. The main difference between traditional datasets and network datasets is the presence of the relational components (links) between instances (nodes) of the network. These links and nodes induce intricate local and global patterns, defining the topology of a network. The topology is ever evolving, determining the dynamics of such a networked system. The work presented in this thesis starts with an extensive analysis of three standard network models, in terms of their properties and self-interactions as well as the size and density of the resultant graphs. These crucial analysis and understanding of the main network models are utilised to later develop a comprehensive network simulation framework. A set of novel nature-inspired link prediction approaches are then developed to predict the evolution of networks, based solely on their topologies. Building on top of these approaches, enhanced topological representations of networks are subsequently combined with node characteristics for the purpose of node classification. Finally, the proposed classification methods are extensively evaluated using simulated networks from our network simulation framework as well as two real-world citation networks. The link prediction approaches proposed in this research show that the topology of the network can be further exploited to improve the prediction of future relationships. Moreover, this research demonstrates the potential of blending state-of-the-art Machine Learning techniques with graph theory. To accelerate such advancements in the field of network science, this research also offers an open- source software to provide high-quality synthetic datasets

On the effects of firing memory in the dynamics of conjunctive networks

Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel or \emph{synchronous} to \emph{asynchronous.} However, studying each possible dynamics defined by different update schemes might not be efficient. In this context, considering some type of temporal delay in the dynamics of Boolean networks emerges as an alternative approach. In this paper, we focus in studying the effect of a particular type of delay called \emph{firing memory} in the dynamics of Boolean networks. Particularly, we focus in symmetric (non-directed) conjunctive networks and we show that there exist examples that exhibit attractors of non-polynomial period. In addition, we study the prediction problem consisting in determinate if some vertex will eventually change its state, given an initial condition. We prove that this problem is {\bf PSPACE}-complete

Predicting epidemic evolution on contact networks from partial observations

The massive employment of computational models in network epidemiology calls for the development of improved inference methods for epidemic forecast. For simple compartment models, such as the Susceptible-Infected-Recovered model, Belief Propagation was proved to be a reliable and efficient method to identify the origin of an observed epidemics. Here we show that the same method can be applied to predict the future evolution of an epidemic outbreak from partial observations at the early stage of the dynamics. The results obtained using Belief Propagation are compared with Monte Carlo direct sampling in the case of SIR model on random (regular and power-law) graphs for different observation methods and on an example of real-world contact network. Belief Propagation gives in general a better prediction that direct sampling, although the quality of the prediction depends on the quantity under study (e.g. marginals of individual states, epidemic size, extinction-time distribution) and on the actual number of observed nodes that are infected before the observation time

Global and partitioned reconstructions of undirected complex networks

It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned reconstructions) are proposed to infer the structure of undirected networks from dynamics. These approaches are applied to evolutionary games occurring on both homogeneous and heterogeneous networks via compressed sensing, which can more efficiently achieve higher reconstruction accuracy with relatively small amounts of data. Our approaches provide different perspectives on effectively reconstructing complex networks.Comment: 6 pages, 2 figures, 1 table; revised version; added numerical results of the PR in Table 1 and expanded Section 4; added 7 reference

Link Prediction in Complex Networks: A Survey

Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labelled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.Comment: 44 pages, 5 figure