Related papers: Maximum Leaf Spanning Trees of Growing Sierpinski …
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in…
We consider the problem of finding a spanning tree with maximum number of leaves (MaxLeaf). A 2-approximation algorithm is known for this problem, and a 3/2-approximation algorithm when restricted to graphs where every vertex has degree 3…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
In a recent paper, Krapivsky and Redner (Phys. Rev. E, 71 (2005) 036118) proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a…
The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history…
We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
We study the problem of maximizing the number of full degree vertices in a spanning tree $T$ of a graph $G$; that is, the number of vertices whose degree in $T$ equals its degree in $G$. In cubic graphs, this problem is equivalent to…
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we obtain two combinatorial results on the number…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
Real-data networks often appear to have strong modularity, or network-of-networks structure, in which subgraphs of various size and consistency occur. Finding the respective subgraph structure is of great importance, in particular for…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
Network science provides an indispensable theoretical framework for studying the structure and function of real complex systems. Different network models are often used for finding the rules that govern their evolution, whereby the correct…
We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and…
In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use…