相关论文: An algorithm for counting circuits: application to…

Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from…

Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…

In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that…

Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…

We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.…

We present a Markov Chain Monte Carlo method for sampling cycle length in large graphs. Cycles are treated as microstates of a system with many degrees of freedom. Cycle length corresponds to energy such that the length histogram is…

Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…

This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics…

Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The…

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…

We give polynomial-time algorithms for obtaining hamilton circuits in random graphs, G, and random directed graphs, D. If n is finite, we assume that G or D contains a hamilton circuit. If G is an arbitrary graph containing a hamilton…

We present an algorithm for evaluating a linear ``intersection transform'' of a function defined on the lattice of subsets of an $n$-element set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in…

The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We present an efficient…

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…

Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…

We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

Pattern counting in graphs is fundamental to network science tasks, and there are many scalable methods for approximating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer…