Graphs can be used to represent such diverse entities as chemical compounds, transportation networks, and the world wide web. Stochastic graph grammars are compact representations of probability distributions over graphs. We present an algorithm for inferring stochastic graph grammars from data. That is, given a set of graphs that, for example, correspond to a set of chemical compounds, all of ...

We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312-316]. We consider all possible connected undirected graphs of orders three through eight. For each graph, using the Monte Carlo Markov Chain simulations, we determine the fixation probability o...

In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...

The reliability polynomial of a graph gives the probability that remains operational when all its edges could fail independently with certain fixed probability. In general, problem finding uniformly most reliable graphs inside family graphs, is, one whose is at least as large any other family, very difficult. this paper, we study in containing hamiltonian cycle.

iv Acknowledgements v List of Tables vii List of Graphs vii

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Let G be a given graph (modelling a communication network) which we assume suuers from static edge faults: That is we let each edge of G be present independently with probability p (or absent with fault probability f = 1 ? p). In particular we are interested in ro-bustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree. Our r...

Several questions and few answers regarding percolation on finite graphs are presented. The following is a note regarding the asymptotic study of percolation on finite transitive graphs. On the one hand, the theory of percolation on infinite graphs is rather developed, although still with many open problems (See [9]). On the other hand random graphs were deeply studied (see [7]). Finite transit...