相关论文: Peripherality in networks: theory and applications

This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…

In the study of topological indices two negative correlations are well known: that between the number of subtrees and the Wiener index (sum of distances), and that between the Merrifield-Simmons index (number of independent vertex subsets)…

Albertson has defined the irregularity of a simple undirected graph $G=(V,E)$ as $ \irr(G) = \sum_{uv\in E}|d_G(u)-d_G(v)|,$ where $d_G(u)$ denotes the degree of a vertex $u \in V$. Recently, this graph invariant gained interest in the…

For a (molecular) graph, the first multiplicative Zagreb index $\prod_1(G) $ is the product of the square of every vertex degree, and the second multiplicative Zagreb index $\prod_2(G) $ is the product of the products of degrees of pairs of…

Daisy cubes are a class of isometric subgraphs of the hypercubes Q n. Daisy cubes include some previously well known families of graphs like Fibonacci cubes and Lucas cubes. Moreover they appear in chemical graph theory. Two distance…

A (molecular) graph in which all vertices have the same degree is known as a regular graph. According to Gutman, Hansen, and M\'elot [J. Chem. Inf. Model. 45 (2005) 222-230], it is of interest to measure the irregularity of nonregular…

The function or performance of a network is strongly dependent on its robustness, quantifying the ability of the network to continue functioning under perturbations. While a wide variety of robustness metrics have been proposed, they have…

Let $G=(V,E)$ be a simple graph with $n = |V|$ vertices and $m = |E|$ edges. The first and second Zagreb indices are among the oldest and the most famous topological indices, defined as $M_1 = \sum_{i \in V} d_i^2$ and $M_2 = \sum_{(i, j)…

Wiener index, defined as the sum of distances between all unordered pairs of vertices, is one of the most popular molecular descriptors. It is well known that among 2-vertex connected graphs on $n\ge 3$ vertices, the cycle $C_n$ attains the…

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…

The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity…

In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…

The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…

We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity…

We discuss two well known network measures: the overlap weight of an edge and the clustering coefficient of a node. For both of them it turns out that they are not very useful for data analytic task to identify important elements (nodes or…

Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…

Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…

Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…

We study the epidemic source detection problem in contact tracing networks modeled as a graph-constrained maximum likelihood estimation problem using the susceptible-infected model in epidemiology. Based on a snapshot observation of the…

Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…