相关论文: Polynomial Time Symmetry and Isomorphism Testing f…

An unweighted, undirected graph $G$ on $n$ nodes is said to have \emph{bandwidth} at most $k$ if its nodes can be labelled from $0$ to $n - 1$ such that no two adjacent nodes have labels that differ by more than $k$. It is known that one…

As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…

We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space.…

In recent work, Rosenbaum and Wagner showed that isomorphism of explicitly listed $p$-groups of order $n$ could be tested in $n^{\frac{1}{2}\log_p n + O(p)}$ time, roughly a square root of the classical bound. The $O(p)$ term is entirely…

The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…

A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for…

We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs…

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…

We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…

Measuring robustness is a fundamental task for analyzing the structure of complex networks. Indeed, several approaches to capture the robustness properties of a network have been proposed. In this paper we focus on spectral graph theory…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…

We study binomiality of the steady state ideals of chemical reaction networks. Considering rate constants as indeterminates, the concept of unconditional binomiality has been introduced and an algorithm based on linear algebra has been…

Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly…

The notion of resistance distance, introduced by Klein and Randi\'c, has become a fundamental concept in spectral graph theory and network analysis, as it captures both the structural and electrical properties of a graph. The associated…

Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…

A classical difficult isomorphism testing problem is to test isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. It is known that this problem can be reduced to solving the alternating matrix space…

Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…

This paper considers the graph signal processing problem of anomaly detection in time series of graphs. We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of…

In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…