Related papers: Size-varying reversible causal graph dynamics
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to…
We connect two seemingly unrelated problems in graph theory. Any graph $G$ has an associated neighborhood multiset $\mathscr{N}(G)= \{N(x) \mid x\in V(G)\}$ whose elements are precisely the open vertex-neighborhoods of $G$. In general there…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
We study the problem of clustering nodes in a dynamic graph, where the connections between nodes and nodes' cluster memberships may change over time, e.g., due to community migration. We first propose a dynamic stochastic block model that…
Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the…
One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65--110, 1995], also known as the weak structure theorem, revealed the local structure of graphs…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
Given a finite undirected graph $X$, a vertex is $0$-dismantlable if its open neighbourhood is a cone and $X$ is $0$-dismantlable if it is reducible to a single vertex by successive deletions of $0$-dismantlable vertices. By an iterative…
Switching about a vertex in a digraph means to reverse the direction of every edge incident with that vertex. Bondy and Mercier introduced the problem of whether a digraph can be reconstructed up to isomorphism from the multiset of…
The richness of quantum theory's reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory's reversible dynamics, its local state space and the degree of non-locality…
Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components…
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…
Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs.…