相关论文: The structure connectivity of Data Center Networks

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

Let $G$ be a graph with a spanning subgraph $F$, let $m$ be a positive integer, and let $f$ be a positive integer-valued function on $V(G)$. In this paper, we show that if for all $S\subseteq V(G)$, $$\Omega_m(G\setminus S)\le \sum_{v\in…

Reliability evaluation and fault tolerance of an interconnection network of some parallel and distributed systems are discussed separately under various link-faulty hypotheses in terms of different $\mathcal{P}$-conditional…

Let $G$ be a connected graph. The edge-connectivity of $G$, denoted by $\lambda(G)$, is the minimum number of edges whose removal renders $G$ disconnected. Let $\delta(G)$ be the minimum degree of $G$. It is well-known that $\lambda(G) \leq…

Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…

We revisit the vertex-failure connectivity oracle problem. This is one of the most basic graph data structure problems under vertex updates, yet its complexity is still not well-understood. We essentially settle the complexity of this…

Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different…

Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the…

We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's…

A graph is non-trivial if it contains at least one nonloop edge. The essential connectivity of $G$, denoted by $\kappa'(G)$, is the minimum number of vertices of $G$ whose removal produces a disconnected graph with at least two components…

Networks are largely used for modelling and analysing data and relations among them. Recently, it has been shown that the use of a single network may not be the optimal choice, since a single network may misses some aspects. Consequently,…

For a compact set $E \subset \mathbb R^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k+1$ points in $E$ such that the distance between a pair of points is specified if the corresponding…

This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <=…

The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a natural generalization of the concept of connectivity $\kappa(G)$, which is just for $k=2$. Total graph is generalized line graph and a large…

We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…

Collecting and analyzing of network traffic data (network telemetry) plays a critical role in managing modern networks. Network administrators analyze their traffic to troubleshoot performance and reliability problems, and to detect and…

Let $G$ be a finite graph and $\kappa(G)$ the vertex connectivity of $G$. A chordal graph $G$ is called chordal$^*$ if no vertex of $G$ is adjacent to all other vertices of $G$. Using the syzygy theory in commutative algebra, it is proved…

One of the most intriguing findings in the structure of neural network landscape is the phenomenon of mode connectivity: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity…

Cosmic connectivity and multiplicity, i.e. the number of filaments globally or locally connected to a given cluster is a natural probe of the growth of structure and in particular of the nature of dark energy. It is also a critical…