Related papers: Statistical network isomorphism
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…
In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
The following problem has been proposed in [Research problems from the Aveiro workshop on graph spectra, {\em Linear Algebra and its Applications}, {\bf 423} (2007) 172-181.]:\\ (Problem AWGS.4) Let $G_n$ and $G'_n$ be two nonisomorphic…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
This paper studies the matched network inference problem, where the goal is to determine if two networks, defined on a common set of nodes, exhibit a specific form of stochastic similarity. Two notions of similarity are considered: (i)…
It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network,…
Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
Quantifying the similarity between two networks is critical in many applications. A number of algorithms have been proposed to compute graph similarity, mainly based on the properties of nodes and edges. Interestingly, most of these…
The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of…
We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a…
Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations,…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at most k in polynomial time. As the clique width of a graph is bounded in terms of its rank width, we also obtain a polynomial time isomorphism test…