1,900 research outputs found
Optimal redundancy against disjoint vulnerabilities in networks
Redundancy is commonly used to guarantee continued functionality in networked
systems. However, often many nodes are vulnerable to the same failure or
adversary. A "backup" path is not sufficient if both paths depend on nodes
which share a vulnerability.For example, if two nodes of the Internet cannot be
connected without using routers belonging to a given untrusted entity, then all
of their communication-regardless of the specific paths utilized-will be
intercepted by the controlling entity.In this and many other cases, the
vulnerabilities affecting the network are disjoint: each node has exactly one
vulnerability but the same vulnerability can affect many nodes. To discover
optimal redundancy in this scenario, we describe each vulnerability as a color
and develop a "color-avoiding percolation" which uncovers a hidden
color-avoiding connectivity. We present algorithms for color-avoiding
percolation of general networks and an analytic theory for random graphs with
uniformly distributed colors including critical phenomena. We demonstrate our
theory by uncovering the hidden color-avoiding connectivity of the Internet. We
find that less well-connected countries are more likely able to communicate
securely through optimally redundant paths than highly connected countries like
the US. Our results reveal a new layer of hidden structure in complex systems
and can enhance security and robustness through optimal redundancy in a wide
range of systems including biological, economic and communications networks.Comment: 15 page
Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks
Many real-world networks exhibit degree-assortativity, with nodes of similar
degree more likely to link to one another. Particularly in social networks, the
contribution to the total assortativity varies with degree, featuring a
distinctive peak slightly past the average degree. The way traditional models
imprint assortativity on top of pre-defined topologies is via degree-preserving
link permutations, which however destroy the particular graph's hierarchical
traits of clustering. Here, we propose the first generative model which creates
heterogeneous networks with scale-free-like properties and tunable realistic
assortativity. In our approach, two distinct populations of nodes are added to
an initial network seed: one (the followers) that abides by usual preferential
rules, and one (the potential leaders) connecting via anti-preferential
attachments, i.e. selecting lower degree nodes for their initial links. The
latter nodes come to develop a higher average degree, and convert eventually
into the final hubs. Examining the evolution of links in Facebook, we present
empirical validation for the connection between the initial anti-preferential
attachment and long term high degree. Thus, our work sheds new light on the
structure and evolution of social networks
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