This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum-length routing. More specifically, it is shown that in a large $n$-dimensional hyperbolic ball $B$ of radius $R$ viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is $Θ(1)$, whereas in a Euclidean ball, the same proportion scales as $Θ(1/R^{n−1})$. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as volume$^2 (B)$, whereas the same traffic load scales as volume$^{1+1/n} (B) in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel database and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network.

This paper presents a cache-aware Bloom-filter algorithm with improved cache behavior and lower false-positive rates compared to prior work. The algorithm relies on the power-of-two choice principle to provide a better distribution of set elements in a blocked Bloom filter. Instead of choosing a single block, we insert new elements into the less-loaded of two blocks to achieve a low false-positive rate while performing only two memory accesses on each insert or query operation. The paper also discusses an optimization technique to balance cache effectiveness with the false-positive rate to fine-tune the Bloom-filter properties.

The Internet is a complex network composed of several networks: the autonomous systems. Each of them is designed with the aim of transporting information efficiently. This information is carried over routes, which are discovered by routing protocols, such as the border gateway protocol (BGP). The protocols may find possible paths between nodes whenever they exist, or even find paths satisfying specific constraints, e.g., a certain quality of service (QoS). Here, we study connectivity as a network attribute related to both situations; we provide a formal lower bound to it based on core decomposition and low-complexity algorithms to find it. Then we apply these algorithms to analyze maps obtained from the prominent Internet mapping projects, and use the LaNet-vi open-source software for their visualization.

Scaling-free graphs are often used to describe a class of graphs that have the self-similarity property. The degree sequences of many scaling-free graphs follow the power-law distribution. In this paper,we study the distributions of graphical degree sequences that are invariant under “scaling.” We show that the invariant degree sequence must be a power-law distribution for sparse graphs if we ignore isolated vertices, or more generally, the vertices of degree less than a fixed constant k. We obtain a concentration result on the degree sequence of a random induced subgraph. The case of hypergraphs (or set systems) is also examined.