We explore the characteristics of the cosmic web around Local Group(LG) like pairs using a cosmological simulation in the $\Lambda$CDM cosmology. We use the Hessian of the gravitational potential to classify regions on scales of $\sim 2$ Mpc as a peak, sheet, filament or void. The sample of LG counterparts is represented by two samples of halo pairs. The first is a general sample composed by pairs with similar masses and isolation criteria as observed for the LG. The second is a subset with additional observed kinematic constraints such as relative pair velocity and separation. We find that the pairs in the LG sample with all constraints are: (i) Preferentially located in filaments and sheets, (ii) Located in in a narrow range of local overdensity $0<\delta<2$, web ellipticity $0.1<e<1.0$ and prolateness $-0.4<p<0.4$. (iii) Strongly aligned with the cosmic web. The alignments are such that the pair orbital angular momentum tends to be perpendicular to the smallest tidal eigenvector, $\hat{e}_3$, which lies along the filament direction or the sheet plane. A stronger alignment is present for the vector linking the two halos with the vector $\hat{e}_3$. Additionally, we fail to find a strong correlation of the spin of each halo in the pair with the cosmic web. All these trends are expected to a great extent from the selection on the LG total mass on the general sample. Applied to the observed LG, there is a potential conflict between the alignments of the different planes of satellites and the numerical evidence for satellite accretion along filaments; the direction defined by $\hat{e}_3$. This highlights the relevance of achieving a precise characterization of the place of the LG in the cosmic web in the cosmological context provided by $\Lambda$CDM.

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