Abstract not found

A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large person-to-person

Community detection is an important task for mining the structure and function of complex networks. Generally, there are several different kinds of nodes in a network which are cluster nodes densely connected within communities, as well as some special nodes like hubs bridging multiple communities and outliers marginally connected with a community. In addition, it has been shown that there is a hierarchical structure in complex networks with communities embedded within other communities. Therefore, a good algorithm is desirable to be able to not only detect hierarchical communities, but also identify hubs and outliers. In this paper, we propose a parameter-free hierarchical network clustering algorithm SHRINK by combining the advantages of density-based clustering and modularity optimization methods.

Abstract. Given a contact network that changes over time (say, day vs night connectivity), and the SIS (susceptible/infected/susceptible, flu like) virus propagation model, what can we say about its epidemic threshold? That is, can we determine when a small infection will “take-off ” and create an epidemic? Consequently then, which nodes should we immunize to prevent an epidemic? This is a very real problem, since, e.g. people have different connections during the day at work, and during the night at home. Static graphs have been studied for a long time, with numerous analytical results. Time-evolving networks are so hard to analyze, that most existing works are simulation studies [5]. Specifically, our contributions in this paper are: (a) we formulate the problem by approximating it by a Non-linear Dynamical system (NLDS), (b) we derive the first closed formula for the epidemic threshold of timevarying graphs under the SIS model, and finally (c) we show the usefulness of our threshold by presenting efficient heuristics and evaluate the effectiveness of our methods on synthetic and real data like the MIT reality mining graphs. 1

Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Digg that spread fast enough for one initial spreader to infect hundreds of people, yet end up affecting only 0.1 % of the entire network. We demonstrate two complementary effects that limit the final size of cascades on Digg. First, because of the highly clustered structure of the Digg network, most people who are aware of a story have been exposed to it via multiple friends. This structure lowers the epidemic threshold while also slowing the overall growth of cascades. In addition, we find that the mechanism for social contagion on Digg deviates from standard social contagion models, like the independent cascade model, and this severely curtails the size of social epidemics on Digg. These findings underscore the fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure.

Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shield-value ’ of a specific set of k nodes and (c) a fast algorithm to choose the best such k nodes. We answer all these three questions: we give the justification behind our choices, we show that they agree with intuition as well as recent results in immunology. Moreover, we propose NetShield, a fast and scalable algorithm. Finally, we give experiments on large real graphs, where NetShield achieves tremendous speed savings exceeding 7 orders of magnitude, against straightforward competitors. 1

Diffusion processes taking place in social networks are used to model a number of phenomena, such as the spread of human or computer viruses, and the adoption of products in ‘viral marketing ’ campaigns. It is generally difficult to obtain accurate information about how such spreads actually occur, so a variety of stochastic diffusion models are used to simulate spreading processes in networks instead. We show that a canonical genetic algorithm with a spatially distributed population, when paired with specific forms of Holland’s synthetic hyperplane-defined objective functions, can simulate a large and rich class of diffusion models for social networks. These include standard diffusion models, such as the independent cascade and competing processes models. In addition, our genetic algorithm diffusion model (GADM) can also model complex phenomena such as information diffusion. We demonstrate an application of the GADM to modeling information flow in a large, dynamic social network derived from e-mail headers.

We introduce a new optimization framework to maximize the expected spread of cascades in networks. Our model allows a rich set of actions that directly manipulate cascade dynamics by adding nodes or edges to the network. Our motivating application is one in spatial conservation planning, where a cascade models the dispersal of wild animals through a fragmented landscape. We propose a mixed integer programming (MIP) formulation that combines elements from network design and stochastic optimization. Our approach results in solutions with stochastic optimality guarantees and points to conservation strategies that are fundamentally different from naive approaches. 1

Abstract—Given a network of who-contacts-whom or wholinks-to-whom, will a contagious virus/product/meme spread and ‘take-over ’ (cause an epidemic) or die-out quickly? What will change if nodes have partial, temporary or permanent immunity? The epidemic threshold is the minimum level of virulence to prevent a viral contagion from dying out quickly and determining it is a fundamental question in epidemiology and related areas. Most earlier work focuses either on special types of graphs or on specific epidemiological/cascade models. We are the first to show the G2-threshold (twice generalized) theorem, which nicely de-couples the effect of the topology and the virus model. Our result unifies and includes as special case older results and shows that the threshold depends on the first eigenvalue of the connectivity matrix, (a) for any graph and (b) for all propagation models in standard literature (more than 25, including H.I.V.) [20], [12]. Our discovery has broad implications for the vulnerability of real, complex networks, and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to ‘what-if ’ questions, and simplified design and evaluation of immunization policies. We also demonstrate our result using extensive simulations on one of the biggest available socialcontact graphs containing more than 31 million interactions among more than 1 million people representing the city of Portland, Oregon, USA. I.

Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since traditional percolation thresholds are derived using observation independent Markov chains, the threshold of the posterior should more accurately model the true phase transition of a network, as the updated posterior more accurately tracks the process. These conditions should provide insight into modeling the dynamic response of the updated posterior to active intervention and control policies while monitoring large complex networks. 1