Geodesic
The inertia set of nonnegative symmetric sign pattern with zero diagonal
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 925-934.

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The inertia set of a symmetric sign pattern $A$ is the set $i(A)=\lbrace i(B) \mid B=B^T \in Q(A)\rbrace $, where $i(B)$ denotes the inertia of real symmetric matrix $B$, and $Q(A)$ denotes the sign pattern class of $A$. In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern $A$ in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns $A$ with zero diagonal that require unique inertia.
Classification : 15A18
Keywords: sign pattern; inertia; inertia set; unique inertia 
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     author = {Gao, Yubin and Shao, Yanling},
     title = {The inertia set of nonnegative symmetric sign pattern with zero diagonal},
     journal = {Czechoslovak Mathematical Journal},
     pages = {925--934},
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     volume = {53},
     number = {4},
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     mrnumber = {2018840},
     zbl = {1080.15501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a11/}
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Gao, Yubin; Shao, Yanling. The inertia set of nonnegative symmetric sign pattern with zero diagonal. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 925-934. http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a11/