DYMOND: DYnamic MOtif-NoDes Network Generative Model

Abstract

Motifs, which have been established as building blocks for network structure, move beyond pair-wise connections to capture longerrange correlations in connections and activity. In spite of this, there are few generative graph models that consider higher-order network structures and even fewer that focus on using motifs in models of dynamic graphs. Most existing generative models for temporal graphs strictly grow the networks via edge addition, and the models are evaluated using static graph structure metrics-which do not adequately capture the temporal behavior of the network. To address these issues, in this work we propose DYnamic MOtif-NoDes (DYMOND)-a generative model that considers (i) the dynamic changes in overall graph structure using temporal motif activity and (ii) the roles nodes play in motifs (e.g., one node plays the hub role in a wedge, while the remaining two act as spokes). We compare DYMOND to three dynamic graph generative model baselines on real-world networks and show that DYMOND performs better at generating graph structure and node behavior similar to the observed network. We also propose a new methodology to adapt graph structure metrics to better evaluate the temporal aspect of the network. These metrics take into account the changes in overall graph structure and the individual nodes' behavior over time.

Neighbourhood matching creates realistic surrogate temporal networks

“…Having studied the temporal development, we now turn to structural similarity between the surrogate data and the original networks. We consider ten metrics for structural similarity: number of interactions, density, 34 interacting individuals, 11 versations, 11 S-metric, 44 duration of contacts, 11 edge strength in the projected weighted network, 11 global clustering coefficient, 45,46 assortativity, 47 and average shortest path length 1 (see SI for their definitions). In particular, duration of contacts and edge strength are measures that can be collected for each edge, so we obtain a distribution over all edges.…”

“…18 However, there is currently a dearth of models for generating surrogate networks from scratch that are able to take into account the two dimensions simultaneously. The few works, that do this, rely on temporal motifs, like Dymond 34 and STM, 35 or on deep learning like TagGen. 36 These three models described in detail in Methods, represent the state-of-the-art.…”

DAMNETS: A Deep Autoregressive Model for Generating Markovian Network Time Series

“…Approaches attempting to generate arbitrary network time series have appeared in the machine learning literature, such as the TagGen model [Zhou et al, 2020a], which uses a self-attention mechanism to learn from temporal random walks on a network time series, from which new network time series are subsequently generated. Another very recent algorithm is DYMOND [Zeno et al, 2021], which is a simpler approach that models the arrival times of 3-node motifs, then samples these subgraphs to generate the NTS. It is important to note that both DYMOND and TagGen attempt to solve a slightly different problem; they take as input a single time series G 0 , .…”

“…The synthetic data sets are constructed to demonstrate the capacity of our model to capture network properties widely observed in empirical data, namely community structure and power-law degree distributions. We compare the samples produced by our model to samples from three baseline models, namely the AGE (Attention-Based Graph Evolution) [Fan and Huang, 2020], DYMOND (DYnamic MOtif-NoDes Network Generative Model) [Zeno et al, 2021] and TagGen [Zhou et al, 2020a] models. Note that both TagGen and DYMOND are only designed to produce samples from one observation of a network time series rather than learn a distribution over many trajectories; we therefore train these models separately on each observation in the test set, then produce a sample and aggregate the outputs -a simpler task as they have access to the test dataset and thus do not have to generalise from the training dataset.…”

Scale-Invariant Strength Assortativity of Streaming Butterflies

“…An example is the case of user-product interactions in Alibaba e-commerce services that incurred a processing rate of 470 million event logs per second during a peak interval [88]. Current works study and model the generative patterns of static or aggregated temporal graphs commonly optimized for down stream analytics or ignore (1) multipartite/non-stationary data distributions, (2) emergence patterns (not just existence) of building blocks, and (3) streaming paradigms such as unbounded/time-sensitive updates, evolving streaming rates, and out-of-order/bursty records (e.g., [3,6,12,43,70,112,121,126]). In this paper, we perform statistical analysis over web log streams to infer the key features governing the emergence of the mesoscale building blocks of the bipartite streaming graphs.…”