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The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
There are hierarchical characteristics in the network and how to effectively reveal the hierarchical characteristics in the network is a problem in the research of network structure. If a node is assigned to the community to which it…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
In a Lombardi drawing of a graph the vertices are drawn as points and the edges are drawn as circular arcs connecting their respective endpoints. Additionally, all vertices have perfect angular resolution, i.e., all angles incident to a…
We propose methods for distributed graph-based multi-task learning that are based on weighted averaging of messages from other machines. Uniform averaging or diminishing stepsize in these methods would yield consensus (single task)…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
We present a new family of graphs with remarkable properties. They are obtained by connecting the points of a random walk when their distance is smaller than a given scale. Their degree (number of neighbors) does not depend on the graph's…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
The local optima network model has proved useful in the past in connection with combinatorial optimization problems. Here we examine its extension to the real continuous function domain. Through a sampling process, the model builds a…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graphs is used to characterize directed acyclic graphs. Moreover,…
Knitting, an ancient fiber art, creates a structured fabric consisting of loops or stitches. Publishing hand knitting patterns involves lengthy testing periods and numerous knitters. Modeling knitting patterns with graphs can help expedite…
Numerous social, medical, engineering and biological challenges can be framed as graph-based learning tasks. Here, we propose a new feature based approach to network classification. We show how dynamics on a network can be useful to reveal…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…
With massive amounts of atomic simulation data available, there is a huge opportunity to develop fast and accurate machine learning models to approximate expensive physics-based calculations. The key quantity to estimate is atomic forces,…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…