Related papers: Counting unlabelled multigraphs with three nodes

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

A strongly connected graph is strongly biconnected if after ignoring the direction of its edges we have an undirected graph with no articulation points. A 3-vertex strongly biconnected graph is a strongly biconnected digraph that has the…

This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…

A planar graph can be embedded in a piecewise linear manifold, and the lattice on each linear piece can be colored with 3-coloring. If a planar graph can be colored with multiple 3-coloring, i.e. coloring the graph in pieces with different…

Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…

Prediction of node and graph labels are prominent network science tasks. Data analyzed in these tasks are sometimes related: entities represented by nodes in a higher-level (higher-scale) network can themselves be modeled as networks at a…

Let $G$ be a connected graph on $n$ vertices with adjacency matrix $A_G$. Associated to $G$ is a polynomial $d_G(x_1,\dots, x_n)$ of degree $n$ in $n$ variables, obtained as the determinant of the matrix $M_G(x_1,\dots,x_n)$, where…

The path packing problem is stated finding the maximum number of edge-disjoint paths between predefined pairs of nodes in an undirected multigraph. Such a multigraph together with predefined node pairs is often called a network.

We propose a classification of polyhedra (planar, $3$-connected graphs) according to their type i.e., their set of quantities of common neighbours for each pair of distinct vertices. For every (finite) set of non-negative integers, we…

In the last few years we have witnessed the emergence, primarily in on-line communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is…

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynomial and skein theory. Some examples of the invariant are computed. An unlinked embedded graph is one…

Manual annotation of the labeled data for relation extraction is time-consuming and labor-intensive. Semi-supervised methods can offer helping hands for this problem and have aroused great research interests. Existing work focuses on…

We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi…

Schreier graphs, which possess both a graph structure and a Schreier structure (an edge-labeling by the generators of a group), are objects of fundamental importance in group theory and geometry. We study the Schreier structures with which…

Multi-modal neuroimaging technology has greatlly facilitated the efficiency and diagnosis accuracy, which provides complementary information in discovering objective disease biomarkers. Conventional deep learning methods, e.g. convolutional…

We give a full characterisation of the symmetries of unlabelled triangulations and derive a constructive decomposition of unlabelled triangulations depending on their symmetries. As an application of these results we can deduce a complete…

Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…

Multimodal data pervades various domains, including healthcare, social media, and transportation, where multimodal graphs play a pivotal role. Machine learning on multimodal graphs, referred to as multimodal graph learning (MGL), is…

Graph clustering is a central topic in unsupervised learning with a multitude of practical applications. In recent years, multi-view graph clustering has gained a lot of attention for its applicability to real-world instances where one has…

We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…