Related papers: Comparing Graphs of Different Sizes
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
In this paper, we present some new results describing connections between the spectrum of a regular graph and its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
In this paper, we consider the average size of independent edge sets, also called matchings, in a graph. We characterize the extremal graphs for the average size of matchings in general graphs and trees. In addition, we obtain inequalities…
We study the height of a spanning tree $T$ of a graph $G$ obtained by starting with a single vertex of $G$ and repeatedly selecting, uniformly at random, an edge of $G$ with exactly one endpoint in $T$ and adding this edge to $T$.
This survey on graphs of large girth consists of two parts. The first deals with some aspects of algebraic and extremal graph theory loosely related to the Moore bound. Our point of departure for the second, Ramsey theoretic, part are some…
Eigenvalues of a graph are of high interest in graph analytics for Big Data due to their relevance to many important properties of the graph including network resilience, community detection and the speed of viral propagation. Accurate…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
We consider numbers and sizes of independent sets in graphs with minimum degree at least $d$, when the number $n$ of vertices is large. In particular we investigate which of these graphs yield the maximum numbers of independent sets of…
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
In this paper, we study the average size of independent (vertex) sets of a graph. This invariant can be regarded as the logarithmic derivative of the independence polynomial evaluated at $1$. We are specifically concerned with extremal…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
Firstly, for a general graph, we find a recursion formula on the number of Hamiltonian cycles and one on cycles. By this result, we give some new polynomial invariants. Secondly, we give a condition to tell whether a polynomial defined by…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
We characterize the bipartite graphs that minimize the (first-degree based) entropy, among all bipartite graphs of given size, or given size and (upper bound on the) order. The extremal graphs turn out to be complete bipartite graphs, or…
Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
How does neural connectivity in autistic children differ from neural connectivity in healthy children or autistic youths? What patterns in global trade networks are shared across classes of goods, and how do these patterns change over time?…