Many known networks have structure of affiliation networks, where each of$n$network nodes (actors) selects an attribute set from a given collection of$m$attributes, and two nodes (actors) establish adjacency relation whenever they share a common attribute. We study the behavior of a random walk on such networks. For this purpose, we use a common model of such networks, a random intersection graph. We establish the cover time of the simple random walk on the binomial random intersection graph${\mathcal{ G}}(n,m,p)$at the connectivity threshold and above it. We consider the range of$(n,m,p)$, where the typical attribute is shared by a (stochastically) bounded number of actors.

The Central European Conferences on Cryptology (CECC) were inaugurated in 2000 at the 14th Czech and Slovak International Conference on Number Theory in Liptovský Ján, Slovak Republic with a special crypto session.Since 2001 the CECC have been organized every year in a selected Central European country: in the Slovak Republic (three times), in Hungary and the Czech Republic (twice each), and in Poland and Austria (once each).The jubilee 10th CECC was held in Poland in 2010.The conference was organized by the Stefan Banach

Abstract We study a connectivity property of a secure wireless network that uses random pre‐distribution of keys. A network is composed of n sensors. Each sensor is assigned a collection of d different keys drawn uniformly at random from a given set of m keys. Two sensors are joined by a communication link if they share a common key. We show that for large n with high probability the connected component of size Ω( n ) emerges in the network when the probability of a link exceeds the threshold 1/ n . Similar component evolution is shown for networks where sensors communicate if they share at least s common keys. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009