Related papers: On the Augmented Zagreb Index
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
The generalized $H(n)$ Hirsch index of order $n$ has been recently introduced and shown to interpolate between the degree and the $K$-core centrality in networks. We provide a detailed analytical characterization of the properties of sets…
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…
Rings comprising chemically bonded atoms are essential topological motifs for the structural ordering of network-forming materials. Quantification of such larger motifs beyond short-range pair correlation is essential for understanding the…
We propose an end-to-end model to predict drug-drug interactions (DDIs) by employing graph-augmented convolutional networks. And this is implemented by combining graph CNN with an attentive pooling network to extract structural relations…
In the preprint arXiv:2511.07900 we proved that there exists a localizing ring $A_M$ for $A$ an associative ring with unit, and $M=\oplus_{i=1}^rM_i$ a direct sum of $r\geq 1$ simple right $A$-modules. For a homomorphism of associative…
We introduce a degree-based variable topological index inspired on the power (or generalized) mean. We name this new index as the mean Sombor index: $mSO_\alpha(G) = \sum_{uv \in E(G)} \left[\left( d_u^\alpha+d_v^\alpha \right) /2…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges $e_1,\cdots,e_m$ is the sum of the numbers $\sqrt{1-2(d_{e_i}+2)^{-1}}$ over $1\le i \le m$, where $d_{e_i}$ is the number of edges adjacent with $e_i$. In this paper, we…
In this work a field theoretical model is constructed to describe the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. As an application, the effects of the…
Recently, graphs have been widely used to represent many different kinds of real world data or observations such as social networks, protein-protein networks, road networks, and so on. In many cases, each node in a graph is associated with…
The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…
Quantum interference (QI) effects in molecular systems are a topic of emerging interest in electron transport studies of single molecule junctions. In a recent Letter, Xia et al. employed a graphical scheme introduced by my colleagues and…
Adoption of recently developed methods from machine learning has given rise to creation of drug-discovery knowledge graphs (KG) that utilize the interconnected nature of the domain. Graph-based modelling of the data, combined with KG…
The group of extensions (as in the title), endowed with something like a connection at Archimedean infinity, is isomorphic to the ad\'ele-class group of $\Q$: which is a topological group with interesting Haar measure.}
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
Analysis of chemical graphs is becoming a major research topic in computational molecular biology due to its potential applications to drug design. One of the major approaches in such a study is inverse quantitative structure…