A dynamic network in a dynamic population: asymptotic properties

• We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Degree correlation

dynamic network

phase transition

random graph

stationary distribution

Degree correlation

Publication and Content Type

art (subject category)

ref (subject category)