Related papers: Katz similarity index comparisons
Measure the similarity of the nodes in the complex networks have interested many researchers to explore it. In this paper, a new method which is based on the degree centrality and the Relative-entropy is proposed to measure the similarity…
We characterize the graphs for which the independence number equals the packing number. As a consequence we obtain simple structural descriptions of the graphs for which (i) the distance-$k$-packing number equals the distance-$2k$-packing…
Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.…
Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. It found considerable applications in a variety of fields. In this paper, we determine the minimum Kirchhoff…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz…
The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Network node similarity measure has been paid particular attention in the field of statistical physics. In this paper, we utilize the concept of information and information loss to measure the node similarity. The whole model is based on…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…
A graph is said to be equimatchable if all its maximal matchings are of the same size. In this work we introduce two extensions of the property of equimatchability by defining two new graph parameters that measure how far a graph is from…
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of…
The $k$-th power of the adjacency matrix of a simple undirected graph represents the number of walks with length $k$ between pairs of nodes. As a walk where no node repeats, a path is a walk where each node is only visited once. The set of…