Doctor of Philosophy / Department of Electrical and Computer Engineering / Pietro Poggi-Corradini / Caterina M. Scoglio / The modulus of a family of walks quanti es the richness of the family by favoring having many short walks over a few longer ones. In this dissertation, we investigate various families of walks to study new measures for quantifying network properties using modulus. The proposed new measures are compared to other known quantities. Our proposed method is based on walks on a network, and therefore will work in great generality. For instance, the networks we consider can be directed, multi-edged, weighted, and even contain disconnected parts. We study the popular centrality measure known in some circles as information centrality, also known as e ective conductance centrality. After reinterpreting this measure in terms of modulus of families of walks, we introduce a modi cation called shell modulus centrality, that relies on the egocentric structure of the graph. Ego networks are networks formed around egos with a speci c order of neighborhoods. We then propose e cient analytical and approximate methods for computing these measures on both directed and undirected networks. Finally, we describe a simple method inspired by shell modulus centrality, called general degree, which improves simple degree centrality and could prove to be a useful tool for practitioners in the applied sciences. General degree is useful for detecting the best set of nodes for immunization. We also study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link-usage optimally. We propose weighting networks using these expected link-usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks. Computing loop modulus bene ts from e cient algorithms for nding shortest loops, thus we propose a deterministic combinatorial algorithm that nds a shortest cycle in graphs. The proposed algorithm reduces the worst case time complexity of the existing combinatorial algorithms to O(nm) or O(hkin2 log n) while visiting at most m - n + 1 cycles (size of cycle basis). For most empirical networks with average degree in O(n1􀀀 ) our algorithm is subcubic.