A lot of real world problems can be modeled as traversals on graph, and mining from such traversals has been found useful in several applications. However, previous works considered only traversals on unweighted graph. This paper generalizes this to the case where vertices of graph are given weights to reflect their importance. Under such weight settings, traditional mining algorithms can not b...

Let K(G) be the clique graph of a graph G. A m-weighting of K(G) consists on giving to each m-size subset of its vertices a weight equal to the size of the intersection of the m corresponding cliques of G. The 2weighted clique graph was previously considered by McKee. In this work we obtain a characterization of weighted clique graphs similar to Roberts and Spencer’s characterization for clique...

An extended star is a tree which has only one vertex with degree larger than two. The -center problem in a graph  asks to find a subset  of the vertices of  of cardinality  such that the maximum weighted distances from  to all vertices is minimized. In this paper we consider the -center problem on the unweighted extended stars, and present some properties to find solution.

In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the problem and introduce the Weighted Edge Searching Problem by considering graphswith arbitrary positive integerweights assigned to its edges. We give bounds on the weighted ...

We give laws of large numbers (in the Lp sense) for the total length of the k-nearest neighbours (directed) graph and the j-th nearest neighbour (directed) graph in Rd, d ∈ N, with power-weighted edges. We deduce a law of large numbers for the standard nearest neighbour (undirected) graph. We give the limiting constants, in the case of uniform random points in (0, 1)d, explicitly. Also, we give...

We study the set of probability distributions visited by a continuous-time quantum walk on graphs. An edge-weighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over all probability distributions on the vertices as the weights are varied over non-negative reals. The graph is uniform mixing if it visits the uniform distribut...

We study the set of probability distributions visited by a continuous-time quantum walk on graphs. An edge-weighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over all probability distributions on the vertices as the weights are varied over non-negative reals. The graph is uniform mixing if it visits the uniform distribut...

Previous approaches to select agents to form a team rely on single-agent capabilities, and team performance is treated as a sum of such known capabilities. Motivated by complex team formation situations, we address the problem where both single-agent capabilities may not be known upfront, e.g., as in ad hoc teams, and where team performance goes beyond single-agent capabilities and depends on t...

The problem of graph partitioning or graph clustering refers to a general class of problems that deals with the following task: given a graph G = (V,E), group the vertices of a graph into groups or clusters or communities. (One might be interested in cases where this graph is weighted, directed, etc., but for now let’s consider non-directed, possibly weighted, graphs. Dealing with weighted grap...