of $A_{\mathcal{G}}$. For many large-scale complex networks, the structure of the network can be very intricate [@S01]-[@Pre08] —in many cases not even known exactly— and an explicit eigenvalue decomposition can be very challenging to compute, if not impossible. In many practical settings, instead of having access to the complete network topology, we have access to local neighborhoods of the network structure around a set of nodes. In this context, it is important to understand the impact of local structural information on the eigenvalues of the adjacency matrix. In the rest of the paper, we propose a novel methodology to compute optimal bounds on relevant eigenvalues of $A_{\mathcal{G}}$ from local information regarding the network structure. Our results allow us to study the role of local structural information in the outcome of games with linear best response functions.

Spectral Analysis of the Interaction Matrix\[Spectral Section\]
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We study the relationship between a network’s local structural properties and the smallest eigenvalue of its adjacency matrix. Algebraic graph theory provides us with tools to relate the eigenvalues of a network with its structural properties. Particularly useful is the following well-known result relating the $k$-th spectral moment of $A_{\mathcal{G}}$ with the number of closed walks 