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Suppose there is a message generated at a node $v$ in a network and $v$ decides to pass the message to one of the neighbors $u$, and $u$ next decides to pass the message to one of its own neighbors, and so on. How to relay the message as far as possible with local decisions? To the best of our knowledge no general solution other than randomly picking available adjacent node exists. Here we report some progress. Our first contribution is a new framework called tp-separate chain decomposition for studying network structures. Each tp-separate chain induces a ranking of nodes. We then prove that the ranks can be locally and distributively computed via searching some stable states of certain dynamical systems on the network and can be used to search long paths of a guaranteed length containing any given node. Numerical analyses on a number of typical real-world networks demonstrate the effectiveness of the approach.
What initial trajectory angle maximizes the arc length of an ideal projectile? We show the optimal angle, which depends neither on the initial speed nor on the acceleration of gravity, is the solution x to a surprising transcendental equation: csc(x)
We study the lobby index (l-index for short) as a local node centrality measure for complex networks. The l-inde is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of biological netwo
Governments have long standing interests in preventing market failures and enhancing innovation in strategic industries. Public policy regarding domestic technology is critical to both national security and economic prosperity. Governments often seek
An interrelation between a topological design of network and efficient algorithm on it is important for its applications to communication or transportation systems. In this paper, we propose a design principle for a reliable routing in a store-carry-
This paper studies controlling segregation in social networks via exogenous incentives. We construct an edge formation game on a directed graph. A user (node) chooses the probability with which it forms an inter- or intra- community edge based on a u