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We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
This work addresses synchronization in transient, non-linear stochastic dynamics corresponding to accesses performed by self-avoiding walks originating at each node of a complex network. More specifically, the synchronizability of accesses…
When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
Popular node embedding methods such as DeepWalk follow the paradigm of performing random walks on the graph, and then requiring each node to be proximate to those appearing along with it. Though proved to be successful in various tasks,…
In recent years, graph neural networks (GNNs) have gained increasing popularity and have shown very promising results for data that are represented by graphs. The majority of GNN architectures are designed based on developing new…
Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…
A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
The node2vec random walk has proven to be a key tool in network embedding algorithms. These random walks are tuneable, and their transition probabilities depend on the previous visited node and on the triangles containing the current and…
Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…
We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…
We study the problem of detecting a random walk on a graph from a sequence of noisy measurements at every node. There are two hypotheses: either every observation is just meaningless zero-mean Gaussian noise, or at each time step exactly…
We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure…
Many real-world problems are naturally modeled as heterogeneous graphs, where nodes and edges represent multiple types of entities and relations. Existing learning models for heterogeneous graph representation usually depend on the…