15 research outputs found
Common adversaries form alliances: modelling complex networks via anti-transitivity
Anti-transitivity captures the notion that enemies of enemies are friends,
and arises naturally in the study of adversaries in social networks and in the
study of conflicting nation states or organizations. We present a simplified,
evolutionary model for anti-transitivity influencing link formation in complex
networks, and analyze the model's network dynamics. The Iterated Local
Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step,
and joins anti-clones to the parent node's non-neighbor set. The graphs
generated by ILAT exhibit familiar properties of complex networks such as
densification, short distances (bounded by absolute constants), and bad
spectral expansion. We determine the cop and domination number for graphs
generated by ILAT, and finish with an analysis of their clustering
coefficients. We interpret these results within the context of real-world
complex networks and present open problems
Preferential duplication graphs
We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph
The Iterated Local Transitivity Model for Tournaments
A key generative principle within social and other complex networks is
transitivity, where friends of friends are more likely friends. We propose a
new model for highly dense complex networks based on transitivity, called the
Iterated Local Transitivity Tournament (or ILTT) model. In ILTT and a dual
version of the model, we iteratively apply the principle of transitivity to
form new tournaments. The resulting models generate tournaments with small
average distances as observed in real-world complex networks. We explore
properties of small subtournaments or motifs in the ILTT model and study its
graph-theoretic properties, such as Hamilton cycles, spectral properties, and
domination numbers. We finish with a set of open problems and the next steps
for the ILTT model
Vertex-pursuit in random directed acyclic graphs
We examine a dynamic model for the disruption of information flow in
hierarchical social networks by considering the vertex-pursuit game Seepage
played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block
the movement of an intruder who moves downward from the source node to a sink.
The minimum number of such agents required to block the intruder is called the
green number. We propose a generalized stochastic model for DAGs with given
expected total degree sequence. Seepage and the green number is analyzed in
stochastic DAGs in both the cases of a regular and power law degree sequence.
For each such sequence, we give asymptotic bounds (and in certain instances,
precise values) for the green number