Related papers: How local constraints influence network diameter a…
We use mathematical methods from the theory of tailored random graphs to study systematically the effects of sampling on topological features of large biological signalling networks. Our aim in doing so is to increase our quantitative…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…
We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
Locally checkable labeling problems (LCLs) form the foundation of the modern theory of distributed graph algorithms. First introduced in the seminal paper by Naor and Stockmeyer [STOC 1993], these are graph problems that can be described by…
Detecting specific structures in a network has been a very active theme of research in distributed computing for at least a decade. In this paper, we start the study of subgraph detection from the perspective of local certification.…
We study the local complexity landscape of locally checkable labeling (LCL) problems on constant-degree graphs with a focus on complexities below $\log^* n$. Our contribution is threefold: Our main contribution is that we complete the…
In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific…
Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…
Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal…
In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures to deviate from the locally tree-like behavior of most standard random graph…
The relationship between topology and network throughput of arbitrarily-connected mesh networks is studied. Taking into account nonlinear channel properties, it is shown that throughput decreases logarithmically with physical network size…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
We consider the problem of topology recognition in wireless (radio) networks modeled as undirected graphs. Topology recognition is a fundamental task in which every node of the network has to output a map of the underlying graph i.e., an…
Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…