Comparison of network criticality, algebraic connectivity, and other graph metrics
Proceedings of the 1st Annual Workshop on Simplifying Complex Network for Practitioners
Subgraph sparsification and nearly optimal ultrasparsifiers
Proceedings of the forty-second ACM symposium on Theory of computing
Efficient methods for large resistor networks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Autonomic traffic engineering for network robustness
IEEE Journal on Selected Areas in Communications
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Betweenness centrality and resistance distance in communication networks
IEEE Network: The Magazine of Global Internetworking
Design is as Easy as Optimization
SIAM Journal on Discrete Mathematics
Robust network planning in nonuniform traffic scenarios
Computer Communications
The Kirchhoff indices of join networks
Discrete Applied Mathematics
The Kirchhoff indexes of some composite networks
Discrete Applied Mathematics
SIAM Journal on Scientific Computing
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The effective resistance between two nodes of a weighted graph is the electrical resistance seen between the nodes of a resistor network with branch conductances given by the edge weights. The effective resistance comes up in many applications and fields in addition to electrical network analysis, including, for example, Markov chains and continuous-time averaging networks. In this paper we study the problem of allocating edge weights on a given graph in order to minimize the total effective resistance, i.e., the sum of the resistances between all pairs of nodes. We show that this is a convex optimization problem and can be solved efficiently either numerically or, in some cases, analytically. We show that optimal allocation of the edge weights can reduce the total effective resistance of the graph (compared to uniform weights) by a factor that grows unboundedly with the size of the graph. We show that among all graphs with $n$ nodes, the path has the largest value of optimal total effective resistance and the complete graph has the least.