相关论文: Neighbor selection and hitting probability in smal…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
The problem of link prediction, predicting if two nodes in a network have a connection between them, is a theoretical problem with numerous field-agnostic real-world applications. This paper investigates the efficacy of three classes of…
If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete…
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.…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all…
Locomotion for legged robots poses considerable challenges when confronted by obstacles and adverse environments. Footstep planners are typically only designed for one mode of locomotion, but traversing unfavorable environments may require…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
The presence of hierarchy in many real-world networks is not yet fully explained. Complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
Complex networks are ubiquitous in nature and play a role of paramount importance in many contexts. Internet and the cyberworld, which permeate our everyday life, are self-organized hierarchical graphs. Urban traffic flows on intricate road…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…