Overlapping Feynman subgraphs

MOHCS: Towards Mining Overlapping Highly Connected Subgraphs

Many networks in real-life typically contain parts in which some nodes are more highly connected to each other than the other nodes of the network. The collection of such nodes are usually called clusters, communities, cohesive groups or modules. In graph terminology, it is called highly connected graph. In this paper, we first prove some properties related to highly connected graph. Based on t...

Finding communities by clustering a graph into overlapping subgraphs

We present a new approach to the problem of finding communities: a community is a subset of actors who induce a locally optimal subgraph with respect to a density function defined on subsets of actors. Two different subsets with significant overlap can both be locally optimal, and in this way we may obtain overlapping communities. We design, implement, and test two novel efficient algorithms, R...

Feynman diagrams versus Fermi-gas Feynman emulator

Full subgraphs

Let G = (V,E) be a graph of density p on n vertices. Following Erdős, Luczak and Spencer [11], an m-vertex subgraph H of G is called full if H has minimum degree at least p(m − 1). Let f(G) denote the order of a largest full subgraph of G. If p ( n 2 ) is a positive integer, define fp(n) = min{f(G) : |V (G)| = n, |E(G)| = p ( n 2 ) }. Erdős, Luczak and Spencer [11] proved that if p = 1 2 , then...

Supermanifolds from Feynman graphs

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying...