28 research outputs found
On the Complexity of Role Colouring Planar Graphs, Trees and Cographs
We prove several results about the complexity of the role colouring problem.
A role colouring of a graph is an assignment of colours to the vertices of
such that two vertices of the same colour have identical sets of colours in
their neighbourhoods. We show that the problem of finding a role colouring with
colours is NP-hard for planar graphs. We show that restricting the
problem to trees yields a polynomially solvable case, as long as is either
constant or has a constant difference with , the number of vertices in the
tree. Finally, we prove that cographs are always -role-colourable for
and construct such a colouring in polynomial time
Growth and Containment of a Hierarchical Criminal Network
We model the hierarchical evolution of an organized criminal network via
antagonistic recruitment and pursuit processes. Within the recruitment phase, a
criminal kingpin enlists new members into the network, who in turn seek out
other affiliates. New recruits are linked to established criminals according to
a probability distribution that depends on the current network structure. At
the same time, law enforcement agents attempt to dismantle the growing
organization using pursuit strategies that initiate on the lower level nodes
and that unfold as self-avoiding random walks. The global details of the
organization are unknown to law enforcement, who must explore the hierarchy
node by node. We halt the pursuit when certain local criteria of the network
are uncovered, encoding if and when an arrest is made; the criminal network is
assumed to be eradicated if the kingpin is arrested. We first analyze
recruitment and study the large scale properties of the growing network; later
we add pursuit and use numerical simulations to study the eradication
probability in the case of three pursuit strategies, the time to first
eradication and related costs. Within the context of this model, we find that
eradication becomes increasingly costly as the network increases in size and
that the optimal way of arresting the kingpin is to intervene at the early
stages of network formation. We discuss our results in the context of dark
network disruption and their implications on possible law enforcement
strategies.Comment: 16 pages, 11 Figures; New title; Updated figures with color scheme
better suited for colorblind readers and for gray scale printin
Core-periphery structure in networks (revisited)
Intermediate-scale (or 'meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of meso-scale network features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as coreperiphery structure, which consists of an identification of a network's nodes into a densely connected core and a sparsely connected periphery. In contrast to traditional network communities, the nodes in a core are also reasonably well-connected to those in the periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account, thereby enabling a detailed description of core-periphery structure. We illustrate the differences between our method and existing methods for identifying which nodes belong to a core, and we use it to classify the most important nodes using examples of friendship, collaboration, transportation, and voting networks
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Growth and containment of a hierarchical criminal network.
We model the hierarchical evolution of an organized criminal network via antagonistic recruitment and pursuit processes. Within the recruitment phase, a criminal kingpin enlists new members into the network, who in turn seek out other affiliates. New recruits are linked to established criminals according to a probability distribution that depends on the current network structure. At the same time, law enforcement agents attempt to dismantle the growing organization using pursuit strategies that initiate on the lower level nodes and that unfold as self-avoiding random walks. The global details of the organization are unknown to law enforcement, who must explore the hierarchy node by node. We halt the pursuit when certain local criteria of the network are uncovered, encoding if and when an arrest is made; the criminal network is assumed to be eradicated if the kingpin is arrested. We first analyze recruitment and study the large scale properties of the growing network; later we add pursuit and use numerical simulations to study the eradication probability in the case of three pursuit strategies, the time to first eradication, and related costs. Within the context of this model, we find that eradication becomes increasingly costly as the network increases in size and that the optimal way of arresting the kingpin is to intervene at the early stages of network formation. We discuss our results in the context of dark network disruption and their implications on possible law enforcement strategies