Related papers: Motivo: fast motif counting via succinct color cod…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
Estimating the frequency of sub-graphs is of importance for many tasks, including sub-graph isomorphism, kernel-based anomaly detection, and network structure analysis. While multiple algorithms were proposed for full enumeration or…
We present a procedure for efficiently sampling colors in the {\congest} model. It allows nodes whose number of colors exceeds their number of neighbors by a constant fraction to sample up to $\Theta(\log n)$ semi-random colors unused by…
Recently, interest has grown in exploring the hypothesis that neural activity conveys information through precise spiking motifs. To investigate this phenomenon, various algorithms have been proposed to detect such motifs in Single Unit…
Graph workloads pose a particularly challenging problem for query optimizers. They typically feature large queries made up of entirely many-to-many joins with complex correlations. This puts significant stress on traditional cardinality…
We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on $n$ vertices. Our algorithm solves a more general problem: given $n$ and $\omega$ as input, it computes the number of…
Color modelling and extraction is an important topic in fashion, art, and design. Recommender systems, color-based retrieval, decorating, and fashion design can benefit from color extraction tools. Research has shown that modeling color so…
Clustering is an essential technique for network analysis, with applications in a diverse range of fields. Although spectral clustering is a popular and effective method, it fails to consider higher-order structure and can perform poorly on…
The identification of motifs--subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks--has become a ubiquitous method for uncovering potentially important subunits within networks…
The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a…
We consider the explanation problem of Graph Neural Networks (GNNs). Most existing GNN explanation methods identify the most important edges or nodes but fail to consider substructures, which are more important for graph data. The only…
A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \(…
We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
Graph Neural Networks (GNNs) are a predominant method for graph representation learning. However, beyond subgraph frequency estimation, their application to network motif significance-profile (SP) prediction remains under-explored, with no…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
Physical and functional constraints on biological networks lead to complex topological patterns across multiple scales in their organization. A particular type of higher-order network feature that has received considerable interest is…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…