Related papers: The idemetric property: when most distances are (a…
The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from today's perspective his model has several severe…
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…
We initiate a thorough study of \emph{distributed property testing} -- producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called \emph{dense} testing model we emulate…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation…
We consider isomorphism properties of infinite random geometric graphs defined over a variety of metrics. In previous work, it was shown that for $\mathbb{R}^n$ with the $L_{\infty}$-metric, the infinite random geometric graph is, with…
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…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We introduce the graph theoretical parameter of edge treewidth. This parameter occurs in a natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of treewidth. We study the combinatorial properties of…
Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the traditional uniform random graph models. In this paper we introduce a new,…
We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
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 -…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…