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Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility.…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…
We study here the social network generated by the asynchronous visits, to a fixed set of sites, of mobile agents modelled as independent random walks on the plane lattice. The social network is constructed by assuming that a group of agents…
In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of…
Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of…
In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible…
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…
We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…