#Deltagraph wikipedia how to#

Large-scale and high resolution data from dynamic processes over networks are becoming increasing available nowadays from online social platforms, such as Twitter and Facebook. Dynamic Processes Over Information Networks: Representation, Modeling, Learning and Inference We apply these results to synthetic and empirical networks, including a study of anomaly detection for the Enron email corpus.

#Deltagraph wikipedia how to#

Our results indicate good practices in the context of community detection for how to aggregate network layers, threshold pairwise-interaction data matrices, and discretize time-varying network data. We identify layer-aggregation strategies that are optimal in that they minimize the detectability limit. We analyze detectability phase transitions that are onset by varying either the density of within-community edges or community size. We explore two methods for aggregation: summing the layers’ adjacency matrices as well as thresholding this summation at some value. Aggregation is often beneficial when the layers are correlated, and it represents a crucial step for the discretization of time-varying network data, whereby layers are binned into time windows. We analyze fundamental limitations on the detectability of communities by developing random matrix theory for the dominant eigenvectors of modularity matrices that encode an aggregation of network layers. Inspired by real-world networks consisting of layers that encode different types of connections, such as a social network at different instances in time, we study community structure in multilayer networks.

Mucha, University of North Carolina at Chapel Hill Enhanced Community Detection in Multilayer and Temporal Networks through Layer Aggregationĭane Taylor, University of North Carolina at Chapel Hill Rajmonda Caceres, Massachusetts Institute of Technology Peter J. The talk is based on recent work in collaboration with Christine Klymko (LLNL) and Francesca Arrigo (Strathclyde). Finally, I will discuss efficient edge modification strategies (including edge removal, addition, and rewiring) that can be used to obtain networks with desirable communicability properties. I will introduce the notion of total communicability of a network as a measure of network connectivity and robustness and show that it can be computed very quickly even for large graphs. These measures can be given an elegant closed form in terms of functions of the adjacency matrix. In this talk I will review some network centrality and communicability measures based on walks. Walk-Based Centrality and Communicability Measures: Algorithms and Applications Numerical results on a variety of synthetic and real-world networks will be presented. This approach gives rise to a class of novel and scalable algorithms that work effectively for large-scale and dense networks. This system is analogous to the Fokker-Planck equation in continuous space, and the solution readily yields the desired influence. We develop a novel and transformative framework that adaptively aggregates the activation states of the network according to the number of active nodes, leading to the construction of a system of differential equations that governs the time evolution of the state probabilities. We consider the problem of predicting influence, defined as the expected number of infected nodes, resulted from information propagating from any given set of source nodes on a network. MS7 Influence Prediction for Continuous-Time Information Propagation on Networks Using Graph-Based Fokker-Planck Equation.Haomin Zhou, Georgia Institute of Technology.

Hongyuan Zha, Georgia Institute of Technology.

This mini-symposium focuses on the recent advances of mathematical modeling and numerical methods as well as their applications in modern network science. New models and computational methods must tackle challenges of inhomogeneous structures of networks, randomness of dynamics, and noise in data.

In these applications, big data is often generated, collected, stored and/or processed in large-scale heterogeneous networks. In recent years, there has been high demand for novel and accurate mathematical models, and fast, stable and scalable computational techniques to address problems emerging from applications on real-world networks, such as social media and power grids.