Related papers: Structural properties and average tapping time on …
We provide an explicit formula for the global mean first-passage time (GMFPT) for random walks in a general graph with a perfect trap fixed at an arbitrary node, where GMFPT is the average of mean first-passage time to the trap over all…
Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomass\'e and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while…
Let $G=(V,E)$ be a simple connected graph. A matching of $G$ is a set of disjoint edges of $G$. For every $n, m\in\mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{\frac{1}{n}}$ which is constructed by replacing each edge of $G$…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
We say that a graph $G$ is $(2,m)$-linked if, for any distinct vertices $a_1,\ldots, a_m, b_1,b_2$ in $G$, there exist vertex disjoint connected subgraphs $A,B$ of $G$ such that $\{a_1, \ldots, a_m\}$ is contained in $A$ and $\{b_1,b_2\}$…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
We develop a general procedure that finds recursions for statistics counting isomorphic copies of a graph $G_0$ in the common random graph models ${\cal G}(n,m)$ and ${\cal G}(n,p)$. Our results apply when the average degrees of the random…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrary graphs. In detail, let $G$ be a connected graph on $k$…
The cover time of random walks on a graph has found wide practical applications in different fields of computer science, such as crawling and searching on the World Wide Web and query processing in sensor networks, with the application…
A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of…
We show that for any fixed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
Many known networks have structure of affiliation networks, where each of $n$ network's nodes (actors) selects an attribute set from a given collection of $m$ attributes and two nodes (actors) establish adjacency relation whenever they…
In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…