Related papers: Continuous Average Straightness in Spatial Graphs
We study the algorithmic problem of computing drawings of graphs in which $(i)$ each vertex is a disk with fixed radius $\rho$, $(ii)$ each edge is a straight-line segment connecting the centers of the two disks representing its…
This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
Strict outerconfluent drawing is a style of graph drawing in which vertices are drawn on the boundary of a disk, adjacencies are indicated by the existence of smooth curves through a system of tracks within the disk, and no two adjacent…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
An obstacle representation of a graph is a mapping of the vertices onto points in the plane and a set of connected regions of the plane (called obstacles) such that the straight-line segment connecting the points corresponding to two…
Summarization is a widespread method for handling very large graphs. The task of structural graph summarization is to compute a concise but meaningful synopsis of the key structural information of a graph. As summaries may be used for many…
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths…
Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…
Graphs (networks) are an important tool to model data in different domains. Real-world graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to…
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
Spanning Centrality is a measure used in network analysis to determine the importance of an edge in a graph based on its contribution to the connectivity of the entire network. Specifically, it quantifies how critical an edge is in terms of…
In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. Precisely, we compute the norm of the vector of eigenvalues of…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this…
Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness…