241 research outputs found
Network Discovery by Generalized Random Walks
We investigate network exploration by random walks defined via stationary and
adaptive transition probabilities on large graphs. We derive an exact formula
valid for arbitrary graphs and arbitrary walks with stationary transition
probabilities (STP), for the average number of discovered edges as function of
time. We show that for STP walks site and edge exploration obey the same
scaling as function of time . Therefore, edge exploration
on graphs with many loops is always lagging compared to site exploration, the
revealed graph being sparse until almost all nodes have been discovered. We
then introduce the Edge Explorer Model, which presents a novel class of
adaptive walks, that perform faithful network discovery even on dense networks.Comment: 23 pages, 7 figure
A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs
One of the simplest ways to decide whether a given finite sequence of
positive integers can arise as the degree sequence of a simple graph is the
greedy algorithm of Havel and Hakimi. This note extends their approach to
directed graphs. It also studies cases of some simple forbidden edge-sets.
Finally, it proves a result which is useful to design an MCMC algorithm to find
random realizations of prescribed directed degree sequences.Comment: 11 pages, 1 figure submitted to "The Electronic Journal of
Combinatorics
Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency
Using the minority game as a model for competition dynamics, we investigate
the effects of inter-agent communications on the global evolution of the
dynamics of a society characterized by competition for limited resources. The
agents communicate across a social network with small-world character that
forms the static substrate of a second network, the influence network, which is
dynamically coupled to the evolution of the game. The influence network is a
directed network, defined by the inter-agent communication links on the
substrate along which communicated information is acted upon. We show that the
influence network spontaneously develops hubs with a broad distribution of
in-degrees, defining a robust leadership structure that is scale-free.
Furthermore, in realistic parameter ranges, facilitated by information exchange
on the network, agents can generate a high degree of cooperation making the
collective almost maximally efficient.Comment: 4 pages, 2 postscript figures include
- …