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Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus quickly retrieve all edges between two sets of nodes (anode-based slice) but cannot quickly retrieve all edges that occur within a given time interval (atime-based slice). We propose a hybrid data structure for storing temporal networks that stores edges in both an adjacency dictionary, enabling rapid node-based slices, and an interval tree, enabling rapid time-based slices. Our hybrid structure also enablescompound slices, where one needs to slice both over nodes and time, either by slicing first over nodes or slicing first over time. We further propose an approach for predictive compound slicing, which attempts to predict whether a node-based or time-based compound slice is more efficient. We evaluate our hybrid data structure on many real temporal network data sets and find that they achieve much faster slice times than existing data structures with only a modest increase in creation time and memory usage.

 

With the prevalence of interaction on social media, data compiled from these networks are perfect for analyzing social trends. One such trend that this paper aims to address is political homophily. Evidence of political homophily is well researched and indicates that people have a strong tendency to interact with others with similar political ideologies. Additionally, as links naturally form in a social network, either through recommendations or indirect interaction, new links are very likely to reinforce communities. This serves to make social media more insulated and ultimately more polarizing. We aim to address this problem by providing link recommendations that will reduce network homophily. We propose several variants of common neighbor-based link prediction algorithms that aim to recommend links to users who are similar but also would decrease homophily. We demonstrate that acceptance of these recommendations can indeed reduce the homophily of the network, whereas acceptance of link recommendations from a standard common neighbors algorithm does not. 

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models. 

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks. 

We consider the problem of analyzing timestamped relational events between a set of entities, such as messages between users of an on-line social network. Such data are often analyzed using static or discrete-time network models, which discard a significant amount of information by aggregating events over time to form network snapshots. In this paper, we introduce a block point process model (BPPM) for continuous-time event-based dynamic networks. The BPPM is inspired by the well-known stochastic block model (SBM) for static networks. We show that networks generated by the BPPM follow an SBM in the limit of a growing number of nodes. We use this property to develop principled and efficient local search and variational inference procedures initialized by regularized spectral clustering. We fit BPPMs with exponential Hawkes processes to analyze several real network data sets, including a Facebook wall post network with over 3,500 nodes and 130,000 events. 

Understanding mechanisms driving link formation in dynamic social networks is a long-standing problem that has implications to understanding social structure as well as link prediction and recommendation. Social networks exhibit a high degree of transitivity, which explains the successes of common neighbor-based methods for link prediction. In this paper, we examine mechanisms behind link formation from the perspective of an ego node. We introduce the notion of personalized degree for each neighbor node of the ego, which is the number of other neighbors a particular neighbor is connected to. From empirical analyses on four on-line social network datasets, we find that neighbors with higher personalized degree are more likely to lead to new link formations when they serve as common neighbors with other nodes, both in undirected and directed settings. This is complementary to the finding of Adamic and Adar that neighbor nodes with higher (global) degree are less likely to lead to new link formations. Furthermore, on directed networks, we find that personalized out-degree has a stronger effect on link formation than personalized in-degree, whereas global in-degree has a stronger effect than global out-degree. We validate our empirical findings through several link recommendation experiments and observe that incorporating both personalized and global degree into link recommendation greatly improves accuracy. 

Contagious processes on networks, such as spread of disease through physical proximity or information diffusion over social media, are continuous-time processes that depend upon the pattern of interactions between the individuals in the network. Continuous-time stochastic epidemic models are a natural fit for modeling the dynamics of such processes. However, prior work on such continuous-time models doesn’t consider the dynamics of the underlying interaction network which involves addition and removal of edges over time. Instead, researchers have typically simulated these processes using discrete-time approximations, in which one has to trade off between high simulation accuracy and short computation time. In this paper, we incorporate continuous-time network dynamics (addition and removal of edges) into continuous-time epidemic simulations. We propose a rejection-sampling based approach coupled with the well-known Gillespie algorithm that enables exact simulation of the continuous-time epidemic process. Our proposed approach gives exact results, and the computation time required for simulation is reduced as compared to discrete-time approximations of comparable accuracy.