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The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the…
The approach of quantifying the damage inflicted on a graph in Albert, Jeong and Barabsi's (AJB) report "Error and Attack Tolerance of Complex Networks" using the size of the largest connected component and the average size of the remaining…
Spectral graph contrastive learning often constructs low- and high-frequency views to capture complementary graph signals, but these views are commonly combined by graph-level or node-agnostic fusion rules. We show that graph-level fusion…
(Im)balance indices can be used to quantify the (im)balance of trees by assigning numerical scores to them. An easy way to generate a new index is to construct a compound index, e.g., a linear combination of established indices. Two of the…
Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…
The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph. This is a generalization of eccentric connectivity…
We consider the problem of uniformity testing of Lipschitz continuous distributions with bounded support. The alternative hypothesis is a composite set of Lipschitz continuous distributions that are at least $\varepsilon$ away in $\ell_1$…
Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we…
Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
While visual comparison of directed acyclic graphs (DAGs) is commonly encountered in various disciplines (e.g., finance, biology), knowledge about humans' perception of graph similarity is currently quite limited. By graph similarity…
We study how the graph structure of the Internet at the Autonomous Systems (AS) level evolved during a decade. For each year of the period 2008-2017 we consider a snapshot of the AS graph and examine how many features related to structure,…
In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree $T=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges, we provide several bounds and exact formulas for these two…
Many models have been proposed to generate Internet Autonomous System (AS) topologies, most of which make structural assumptions about the AS graph. In this paper we compare AS topology generation models with several observed AS topologies.…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
The braid indices of most links remain unknown as there is no known universal method that can be used to determine the braid index of an arbitrary knot. This is also the case for alternating knots. In this paper, we show that if $K$ is an…
It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower…
Information-based complexity (IBC) is a well-defined complexity measure of any object given a description in a language and a classifier that identifies those descriptions with the object. Of course, the exact numerical value will vary…