相关论文: Mostar index of graph operations
The vertex $k$-partiteness $v_k(G)$ of graph $G$ is defined as the fewest number of vertices whose deletion from $G$ yields a $k$-partite graph. In this paper, we introduce two concepts: monotonic decreasing topological index and monotonic…
The palette of a vertex v in a graph G is the set of colors assigned to the edges incident to v. The palette index of G is the minimum number of distinct palettes among the vertices, taken over all proper edge colorings of G. This paper…
Continuing the recent work of L. Zhong and K. Xu [MATCH Commun. Math. Comput. Chem.71(2014) 627-642], we determine inequalities among several vertex-degree-based topological indices; first geometric-arithmetic index(GA), augmented Zagreb…
Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…
There are several metrics (Modularity, Mutual Information, Conductance, etc.) to evaluate the strength of graph clustering in large graphs. These metrics have great significance to measure the effectiveness and they are often used to find…
We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a…
The Sombor indices, a new category of degree-based topological molecular descriptors, have been widely investigated due to their excellent chemical applicability. This paper aims to establish Sombor indices distributions in random polygonal…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
Given a graph $G$, a mutual-visibility coloring of $G$ is introduced as follows. We color two vertices $x,y\in V(G)$ with a same color, if there is a shortest $x,y$-path whose internal vertices have different colors than $x,y$. The smallest…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
In this work we describe and compare the classic inner product and Pearson correlation coefficient as well as the recently introduced real-valued Jaccard and coincidence indices. Special attention is given to diverse schemes for taking into…
Prediction of solubility has been a complex and challenging physiochemical problem that has tremendous implications in the chemical and pharmaceutical industry. Recent advancements in machine learning methods have provided great scope for…
In this paper, we examine roots of graph polynomials where those roots can be considered as structural graph measures. More precisely, we prove analytical results for the roots of certain modified graph polynomials and also discuss…
We compute: * the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), Bestvina-Brady groups, and graph products of groups, * the L^2-Betti numbers of Bestvina-Brady groups and of…
Characterizing motif (i.e., locally connected subgraph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph…
Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that…
A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The study provides tools for…
Kontsevich's graphs allow encoding multi-vectors whose coefficients are differential-polynomial in the coefficients of a given Poisson bracket on an affine real manifold. Encoding formulas by directed graphs adapts to the class of…
The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that…
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and…