Related papers: Harmonic Centralization of Some Graph Families
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…
In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…
Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…
Let $G$ be a finite non abelian group. The centralizer graph of $G$ is a simple undirected graph $\Gamma_{cent}(G)$, whose vertex set consists of proper centralizers of $G$ and two vertices are adjacent if and only if their cardinalities…
Centrality measures have been defined to quantify the importance of a node in complex networks. The relative importance of a node can be measured using its centrality rank based on the centrality value. In the present work, we predict the…
An ecological network is a formal representation of a specific type of interaction in a corresponding ecosystem. Such networks have traditionally been modelled as encoding exclusively pairwise interactions among the fundamental units of…
Eigenvector centrality is a standard network analysis tool for determining the importance of (or ranking of) entities in a connected system that is represented by a graph. However, many complex systems and datasets have natural multi-way…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of graph filters to model network processes, data supported on the…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
The harmonic index of a graph $G$ is defined as the sum of weights $\frac{2}{deg(v) + deg(u)}$ of all edges $uv$ of $E (G)$, where $deg (v)$ denotes the degree of a vertex $v$ in $V (G)$. In this note we generalize results of [L. Zhong, The…
Centrality measures are crucial in quantifying the influence of the members of a social network. Although there has been a great deal of work dealing with this issue, the vast majority of classical centrality measures are agnostic of the…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Eigenvector centrality is a linear algebra based graph invariant used in various rating systems such as webpage ratings for search engines. A generalization of the eigenvector centrality invariant is defined which is motivated by the need…
Many Entity Linking systems use collective graph-based methods to disambiguate the entity mentions within a document. Most of them have focused on graph construction and initial weighting of the candidate entities, less attention has been…
Several expressions for the $j$-th component $\left( x_{k}\right)_{j}$ of the $k$-th eigenvector $x_{k}$ of a symmetric matrix $A$ belonging to eigenvalue $\lambda_{k}$ and normalized as $x_{k}^{T}x_{k}=1$ are presented. In particular, the…
We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…
In the study of the behavior of centrality measures with respect to network modifications, score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc…