Growing distributed networks with arbitrary degree distributions

We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with some mild constraints, it is possible by a suitable choice of rules to arrange for the network to have any degree distribution we desire. We also describe a mechanism based on biased random walks by which appropriate rules could be implemented in practice. As an example application, we describe and simulate the construction of a peer-to-peer network optimized to minimize search times and bandwidth requirements.Comment: 10 pages, 2 figure

Bicomponents and the robustness of networks to failure

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes them to become disconnected. This definition leads us naturally to consider bicomponents, subnetworks in which every node has a robust connection of this kind to every other. Here we study bicomponents in both real and model networks using a combination of exact analytic techniques and numerical methods. We show that standard network models predict there to be essentially no small bicomponents in most networks, but there may be a giant bicomponent, whose presence coincides with the presence of the ordinary giant component, and we find that real networks seem by and large to follow this pattern, although there are some interesting exceptions. We study the size of the giant bicomponent as nodes in the network fail, using a specially developed computer algorithm based on data trees, and find in some cases that our networks are quite robust to failure, with large bicomponents persisting until almost all vertices have been removed.Comment: 5 pages, 1 figure, 1 tabl

A sampling-guided unsupervised learning method to capture percolation in complex networks

The use of machine learning techniques in classical and quantum systems has led to novel techniques to classify ordered and disordered phases, as well as uncover transition points in critical phenomena. Efforts to extend these methods to dynamical processes in complex networks is a field of active research. Network-percolation, a measure of resilience and robustness to structural failures, as well as a proxy for spreading processes, has numerous applications in social, technological, and infrastructural systems. A particular challenge is to identify the existence of a percolation cluster in a network in the face of noisy data. Here, we consider bond-percolation, and introduce a sampling approach that leverages the core-periphery structure of such networks at a microscopic scale, using onion decomposition, a refined version of the $k-$core. By selecting subsets of nodes in a particular layer of the onion spectrum that follow similar trajectories in the percolation process, percolating phases can be distinguished from non-percolating ones through an unsupervised clustering method. Accuracy in the initial step is essential for extracting samples with information-rich content, that are subsequently used to predict the critical transition point through the confusion scheme, a recently introduced learning method. The method circumvents the difficulty of missing data or noisy measurements, as it allows for sampling nodes from both the core and periphery, as well as intermediate layers. We validate the effectiveness of our sampling strategy on a spectrum of synthetic network topologies, as well as on two real-word case studies: the integration time of the US domestic airport network, and the identification of the epidemic cluster of COVID-19 outbreaks in three major US states. The method proposed here allows for identifying phase transitions in empirical time-varying networks.Comment: 16 pages, 6 figure

Urban characteristics attributable to density-driven tie formation

Motivated by empirical evidence on the interplay between geography, population density and societal interaction, we propose a generative process for the evolution of social structure in cities. Our analytical and simulation results predict both super-linear scaling of social tie density and information flow as a function of the population. We demonstrate that our model provides a robust and accurate fit for the dependency of city characteristics with city size, ranging from individual-level dyadic interactions (number of acquaintances, volume of communication) to population-level variables (contagious disease rates, patenting activity, economic productivity and crime) without the need to appeal to modularity, specialization, or hierarchy.Comment: Early version of this paper was presented in NetSci 2012 as a contributed talk in June 2012. An improved version of this paper is published in Nature Communications in June 2013. It has 14 pages and 5 figure

Structural and Dynamical Properties of Complex Networks.

Recent years have witnessed a substantial amount of interest within the physics community in the properties of networks. Techniques from statistical physics coupled with the widespread availability of computing resources have facilitated studies ranging from large scale empirical analysis of the worldwide web, social networks, biological systems, to the development of theoretical models and tools to explore the various properties of these systems. Following these developments, in this dissertation, we present and solve for a diverse set of new problems, investigating the structural and dynamical properties of both model and real world networks.We start by defining a new metric to measure the stability of network structure to disruptions, and then using a combination of theory and simulation study its properties in detail on artificially generated networks; we then compare our results to a selection of networks from the real world and find good agreement in most cases. In the following chapter, we propose a mathematical model that mimics the structure of popular file-sharing websites such as Flickr and CiteULike and demonstrate that many of its properties can solved exactly in the limit of large network size. The remaining part of the dissertation primarily focuses on the dynamical properties of networks. We first formulate a model of a network that evolves under the addition and deletion of vertices and edges, and solve for the equilibrium degree distribution for a variety of cases of interest. We then consider networks whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with some mild constraints, it is possible by a suitable choice of rules to arrange for the network to have any degree distribution we desire. In addition we define a simple local algorithm by which appropriate rules can be implemented in practice. Finally, we conclude our dissertation with a game theory model on social networks that tracks the dynamical evolution of a group of interacting agents such as diplomats or political lobbyists seeking to rise to a position of influence, by balancing competing interests.Ph.D.PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64757/1/gghoshal_1.pd