Detecting degree symmetries in networks

The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping degree sequences. These measures are evaluated on artificial and real networks. Specifically we consider vertices in the human metabolic network. We also measure the average degree-symmetry coefficient for different classes of real-world network. We find that most studied examples are weakly positively degree-symmetric. The exceptions are an airport network (having a negative degree-symmetry coefficient) and one-mode projections of social affiliation networks that are rather strongly degree-symmetric

Dynamic rewiring in small world networks

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us to examine order parameters of our system at total equilibrium, probing both spin- and graph-statistics. Of these, interestingly, the degree distribution is found to acquire a Poisson-like form (both within and outside the ordered phase). Comparison with Glauber simulations confirms our results satisfactorily.Comment: 21 pages, 5 figure

Preferencial growth: exact solution of the time dependent distributions

We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a probability proportional to the size thereof. We calculate exactly the probability \Pm_i(k,t) that the size of the i-th cluster at time t is k. We analyze the asymptotics, the scaling properties of the size distribution and of the mean size as well as the relation of our system to recent network models.Comment: 8 pages, 4 figure

Phase transitions in social sciences: two-populations mean field theory

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction and conclusions from the social sciences perspectives are drawn

Hawks and Doves on Small-World Networks

We explore the Hawk-Dove game on networks with topologies ranging from regular lattices to random graphs with small-world networks in between. This is done by means of computer simulations using several update rules for the population evolutionary dynamics. We find the overall result that cooperation is sometimes inhibited and sometimes enhanced in those network structures, with respect to the mixing population case. The differences are due to different update rules and depend on the gain-to-cost ratio. We analyse and qualitatively explain this behavior by using local topological arguments.Comment: 12 pages, 8 figure

Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study non-clustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small-worlds that includes {\it declustered} networks, and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.Comment: 10 pages and 9 figure

Search in Complex Networks : a New Method of Naming

We suggest a method for routing when the source does not posses full information about the shortest path to the destination. The method is particularly useful for scale-free networks, and exploits its unique characteristics. By assigning new (short) names to nodes (aka labelling) we are able to reduce significantly the memory requirement at the routers, yet we succeed in routing with high probability through paths very close in distance to the shortest ones.Comment: 5 pages, 4 figure

Network growth for enhanced natural selection

Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population tips the balance in favor of natural selection. The probability that the spread occurs, known as the fixation probability, depends heavily on how the population is structured. Certain topologies, albeit highly artificially contrived, have been shown to exist that favor fixation. We introduce a randomized mechanism for network growth that is loosely inspired in some of these topologies' key properties and demonstrate, through simulations, that it is capable of giving rise to structured populations for which the fixation probability significantly surpasses that of an unstructured population. This discovery provides important support to the notion that natural selection can be enhanced over random drift in naturally occurring population structures

Navigability is a Robust Property

The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions

Denying humanness to victims: How gang members justify violent behavior

The high prevalence of violent offending amongst gang-involved youth has been established in the literature. Yet the underlying psychological mechanisms that enable youth to engage in such acts of violence remain unclear. 189 young people were recruited from areas in London, UK, known for their gang activity. We found that gang members, in comparison to non-gang youth, described the groups they belong to as having recognized leaders, specific rules and codes, initiation rituals, and special clothing. Gang members were also more likely than non-gang youth to engage in violent behavior and endorse moral disengagement strategies (i.e., moral justification, euphemistic language, advantageous comparison, displacement of responsibility, attribution of blame, and dehumanization). Finally, we found that dehumanizing victims partially mediated the relationship between gang membership and violent behavior. These findings highlight the effects of groups at the individual level and an underlying psychological mechanism that explains, in part, how gang members engage in violence