Related papers: Triple-loop networks with arbitrarily many minimum…

Let $n\geq 5$ and $m\geq 1$ be positive integers. Let $S = ( s_1, s_2, \ldots , s_m)$ be a sequence of integers such that $1 \leq s_1 < s_2 < \ldots < s_m \leq \lfloor \frac{n-1}{2} \rfloor.$ In this paper, we discuss the diameter of…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…

Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many…

Many real world networks (graphs) are observed to be 'small worlds', i.e., the average path length among nodes is small. On the other hand, it is somewhat unclear what other average path length values networks can produce. In particular, it…

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…

We map the conformation space of a simple lattice polymer chain to a network, where (i) the vertices of the network have a one-to-one correspondence to the conformations of the chain, and (ii) a link between two vertices indicates the…

An algorithm to construct analytic approximations to two-loop diagrams describing their behaviour at small non-zero thresholds is discussed. For some special cases (involving two different-scale mass parameters), several terms of the…

We prove that all $1$-vertex spatial graphs with adequate diagrams have minimal crossing number, and that spatial graph diagrams obtained by replacing vertices and edges of a planar embedded graph by minimal crossing link or spatial graph…

Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA'20] introduced the $\mathsf{HYBRID}$ model, which is based on…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

In this work we study shortest path problems in multimode graphs, a generalization of the min-distance measure introduced by Abboud, Vassilevska W. and Wang in [SODA'16]. A multimode shortest path is the shortest path using one of multiple…

This paper presents methods to compare networks where relationships between pairs of nodes in a given network are defined. We define such network distance by searching for the optimal method to embed one network into another network, prove…

Mixed radial Moore graphs are approximations of mixed Moore graphs that preserve the distance-preserving spanning tree for some vertices. One way to measure their resemblance to a mixed Moore graph is using the status measure. The status of…

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…

We introduce the concept of distance ideals of graphs, which can be regarded as a generalization of the Smith normal form and the spectra of the distance matrix of a graph. We obtain a classification of the graphs with at most one trivial…

The idea of minimum distance, familiar from R <-> 1/R duality when the string target space is a circle, is analyzed for less trivial geometries. The particular geometry studied is that of a blown-up quotient singularity within a Calabi-Yau…

A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…

All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…