Intrinsic brain activity is characterized by highly organized co-activations between different regions, forming clustered spatial patterns referred to as resting-state networks. The observed co-activation patterns are sustained by the intricate fabric of millions of interconnected neurons constituting the brain's wiring diagram. However, as for other real networks, the relationship between the connectional structure and the emergent collective dynamics still evades complete understanding. Here, we show that it is possible to estimate the expected pair-wise correlations that a network tends to generate thanks to the underlying path structure. We start from the assumption that in order for two nodes to exhibit correlated activity, they must be exposed to similar input patterns from the entire network. We then acknowledge that information rarely spreads only along a unique route but rather travels along all possible paths. In real networks, the strength of local perturbations tends to decay as they propagate away from the sources, leading to a progressive attenuation of the original information content and, thus, of their influence. Accordingly, we define a novel graph measure, topological similarity, which quantifies the propensity of two nodes to dynamically correlate as a function of the resemblance of the overall influences they are expected to receive due to the underlying structure of the network. Applied to the human brain, we find that the similarity of whole-network inputs, estimated from the topology of the anatomical connectome, plays an important role in sculpting the backbone pattern of time-average correlations observed at rest. The quest to understand how structure shapes function lies at the heart of a broad spectrum of disciplines, ranging from biology to network science. For over a decade, many efforts have been devoted to investigating the impact of different network features, e.g., hubs, clustering, or communities, on the collective behaviour of dynamical processes on complex networks such as spreading phenomena and synchronization. However, a unique answer to this question is not possible, because the emerging network activity is a product of the interplay between the network's topology, the particular local dynamics governing nodes' behavior, and the coupling function defining how information is transferred: network's topology shapes, but does not determine, the collective dynamics. The question is thus whether we can estimate what is the contribution of the structure alone, and which are the most relevant topological features in sculpting the emergent functional relations. Here, we have shown that the global path structure of the network is what truly determines the contribution of the network over the collective dynamics, as it implicitly incorporates information about all other network features, e.g., degree-distributions or modules. The expected magnitude of synchrony or correlation between two nodes is largely governed by the common inputs they receive from all other nodes, given that information propagates along all possible paths of any length. We quantify this pair-wise, whole-network affinity introducing a network measure, the topological similarity (𝒯T). Formally, 𝒯T is the direct relation between the structure of a network and the pattern of functional relations that it tends to produce. Applied to the human brain, we find that the similarity of whole-network inputs, defined by the topology of the underlying anatomical connectome, plays an important role in sculpting the backbone pattern of time-average correlations observed at rest. This confirms the pivotal relevance of the path structure in sculpting the network's correlations due to spontaneous activity.

This work was supported by (R.G.B.) the FI-DGR scholarship of the Catalan Government through the Agència de Gestió d'Ajuts Universitari i de Recerca, under Agreement No. 2013FI-B1-00099, (G.Z.L.) the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 720270 (HBP SGA1), (G.D.) the European Research Council Advanced Grant: DYSTRUCTURE (295129) and the Spanish Research Project No. PSI2013-42091-P, (Z.K.) European Community's Seventh Framework Programme [FP7/2007-2013] under agreement PITN-GA-2011-290011, (V.M.K.) European Community's Seventh Framework Programme [FP7/2007-2013] under Agreement No. PITN-GA-2012-316746 and (M.L.K.) by the European Research Council Consolidator Grant No. CAREGIVING (615539).