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Counting the number of small subgraphs, called motifs, is a fundamental problem in social network analysis and graph mining. Many real-world networks are directed and temporal, where edges have timestamps. Motif counting in directed,…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
We propose a neural approach for estimating spatially varying light selection distributions to improve importance sampling in Monte Carlo rendering, particularly for complex scenes with many light sources. Our method uses a neural network…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
I run Monte Carlo simulations of content production over random Watts-Strogatz graphs to show various effects relevant to modeling and understanding Randomized Controlled Trials on social networks: the network effect, spillover effect,…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally,…
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…
Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…
A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a…
We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…