Related papers: Fast counting of medium-sized rooted subgraphs

Similarity search approaches based on graph walks have recently attained outstanding speed-accuracy trade-offs, taking aside the memory requirements. In this paper, we revisit these approaches by considering, additionally, the memory…

We consider a weighted counting problem on matchings, denoted $\textrm{PrMatching}(\mathcal{G})$, on an arbitrary fixed graph family $\mathcal{G}$. The input consists of a graph $G\in \mathcal{G}$ and of rational probabilities of existence…

We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…

Let ${\cal G}$ be a minor-closed graph class. We say that a graph $G$ is a $k$-apex of ${\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to ${\cal G}$. We denote by ${\cal A}_k ({\cal G})$ the set…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that…

We present an exact algorithm for computing all common subgraphs with the maximum number of vertices across multiple graphs. Our approach is further extended to handle the connected Maximum Common Subgraph (MCS), identifying the largest…

We consider the problem of enumerating all instances of a given pattern graph in a large data graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges in the data graph, $k=O(1)$…

We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…

Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…

A homomorphism from a graph G to a graph H is a function from V(G) to V(H) that preserves edges. Many combinatorial structures that arise in mathematics and computer science can be represented naturally as graph homomorphisms and as…

This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…

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…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…

Fix $m \in \mathbb N$. A new generalization of the $H$-join operation of a family of graphs $\{G_1, G_2, \dots, G_k\}$ constrained by indexing maps $I_1,I_2,\dots,I_k$ is introduced as $H_m$-join of graphs, where the maps $I_i:V(G_i)$ to…

We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…

Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…

Given a graph $G$, a vertex switch of $v \in V(G)$ results in a new graph where neighbors of $v$ become nonneighbors and vice versa. This operation gives rise to an equivalence relation over the set of labeled digraphs on $n$ vertices. The…

As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…